Bài 2: Định Lí Đảo Và Hệ Quả Của Định Lí Ta-Lét
Hướng dẫn giải Bài 14 (Trang 64 SGK Toán Hình học 8, Tập 2)
<p>Cho ba đoạn thẳng có độ dài là <span id="MathJax-Element-1-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>p</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>p</mi></math></span></span> ( cùng đơn vị đo).</p>
<p>Dựng đoạn thẳng có độ dài <span id="MathJax-Element-2-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>"><span id="MJXc-Node-8" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-9" class="mjx-mrow"><span id="MJXc-Node-10" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span></span></span><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></span></span> sao cho:</p>
<p><strong>LG a.</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⁢</mo><mfrac><mi>x</mi><mi>m</mi></mfrac><mo>=</mo><mn>2</mn></math></p>
<p><strong>Phương pháp giải:</strong></p>
<p>Áp dụng hệ quả của định lý TaLet.</p>
<p><strong>Giải chi tiết:</strong></p>
<p>Cách dựng:</p>
<p>- Vẽ hai tia <span id="MathJax-Element-4-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>x</mi><mo>,</mo><mi>O</mi><mi>y</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>x</mi><mo>,</mo><mi>O</mi><mi>y</mi></math></span></span> không đối nhau.</p>
<p>- Trên tia <span id="MathJax-Element-5-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>x</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>x</mi></math></span></span> lấy hai điểm <span id="MathJax-Element-6-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>,</mo><mspace width="thinmathspace" /><mi>B</mi></math>"><span id="MJXc-Node-31" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-32" class="mjx-mrow"><span id="MJXc-Node-33" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">M</span></span><span id="MJXc-Node-34" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-35" class="mjx-mspace"></span><span id="MJXc-Node-36" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">B</span></span></span></span></span> sao cho <span id="MathJax-Element-7-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>M</mi><mo>=</mo><mn>1</mn><mo>;</mo><mi>O</mi><mi>B</mi><mo>=</mo><mn>2</mn></math>"><span id="MJXc-Node-37" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-38" class="mjx-mrow"><span id="MJXc-Node-39" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">O</span></span><span id="MJXc-Node-40" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">M</span></span><span id="MJXc-Node-41" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-42" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">1</span></span><span id="MJXc-Node-43" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">;</span></span><span id="MJXc-Node-44" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">O</span></span><span id="MJXc-Node-45" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-46" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-47" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">2</span></span></span></span></span> đơn vị.</p>
<p>- Trên tia <span id="MathJax-Element-8-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>y</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>y</mi></math></span></span> lấy điểm A sao cho <span id="MathJax-Element-9-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>A</mi><mo>=</mo><mi>m</mi></math>"><span id="MJXc-Node-52" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-53" class="mjx-mrow"><span id="MJXc-Node-54" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">O</span></span><span id="MJXc-Node-55" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-56" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-57" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">m</span></span></span></span></span> </p>
<p>- Nối <span id="MathJax-Element-10-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mi>A</mi></math>"><span id="MJXc-Node-58" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-59" class="mjx-mrow"><span id="MJXc-Node-60" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">M</span></span><span id="MJXc-Node-61" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span></span></span></span>.</p>
<p>- Vẽ đường thẳng đi qua <span id="MathJax-Element-11-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math></span></span> và song song với <span id="MathJax-Element-12-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mi>A</mi></math>"><span id="MJXc-Node-65" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-66" class="mjx-mrow"><span id="MJXc-Node-67" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">M</span></span></span></span><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></span></span> cắt <span id="MathJax-Element-13-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>y</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>y</mi></math></span></span> tại <span id="MathJax-Element-14-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math>"><span id="MJXc-Node-73" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-74" class="mjx-mrow"><span id="MJXc-Node-75" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span></span></span></span> thì <span id="MathJax-Element-15-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>C</mi><mo>=</mo><mi>x</mi></math>"><span id="MJXc-Node-76" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-77" class="mjx-mrow"><span id="MJXc-Node-78" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">O</span></span><span id="MJXc-Node-79" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-80" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-81" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">x</span></span></span></span></span> là đoạn thẳng cần dựng.</p>
<p>Chứng minh: </p>
<p>Xét tam giác OBC có <span id="MathJax-Element-16-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mi>N</mi><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>B</mi><mi>C</mi></math>"><span id="MJXc-Node-82" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-83" class="mjx-mrow"><span id="MJXc-Node-84" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">M</span></span><span id="MJXc-Node-85" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">N</span></span><span id="MJXc-Node-86" class="mjx-texatom"><span id="MJXc-Node-87" class="mjx-mrow"><span id="MJXc-Node-88" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-89" class="mjx-texatom"><span id="MJXc-Node-90" class="mjx-mrow"><span id="MJXc-Node-91" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-92" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-93" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span></span></span></span> nên:</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>O</mi><mo>⁢</mo><mi>C</mi></mrow><mrow><mi>O</mi><mo>⁢</mo><mi>A</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>O</mi><mo>⁢</mo><mi>B</mi></mrow><mrow><mi>O</mi><mo>⁢</mo><mi>M</mi></mrow></mfrac><mo>⁢</mo></math>(theo hệ quả định lý Talet)</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mfrac><mi>x</mi><mi>m</mi></mfrac><mo>=</mo><mn>2</mn></math></p>
<p><img src="https://img.loigiaihay.com/picture/2018/0718/b14-trang-64-sgk-toan-8-t2-c2.jpg" /></p>
<p><strong>LG b.</strong></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>x</mi><mi>n</mi></mfrac><mo>=</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></math><strong><br /></strong></p>
<p>Áp dụng hệ quả của định lý TaLet.</p>
<p><strong>Giải chi tiết:</strong></p>
<p>Cách dựng: </p>
<p>- Vẽ hai tia <span id="MathJax-Element-20-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>x</mi></math>"><span id="MJXc-Node-138" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-139" class="mjx-mrow"><span id="MJXc-Node-140" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">O</span></span><span id="MJXc-Node-141" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span></span></span></span> và <span id="MathJax-Element-21-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>y</mi></math>"><span id="MJXc-Node-142" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-143" class="mjx-mrow"><span id="MJXc-Node-144" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">O</span></span><span id="MJXc-Node-145" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">y</span></span></span></span></span> không đối nhau.</p>
<p>- Trên tia <span id="MathJax-Element-22-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>x</mi></math>"><span id="MJXc-Node-146" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-147" class="mjx-mrow"><span id="MJXc-Node-148" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">O</span></span><span id="MJXc-Node-149" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span></span></span></span> đặt hai đoạn <span id="MathJax-Element-23-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>A</mi><mo>=</mo><mn>2</mn></math>"><span id="MJXc-Node-150" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-151" class="mjx-mrow"><span id="MJXc-Node-152" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">O</span></span><span id="MJXc-Node-153" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-154" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-155" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">2</span></span></span></span></span> đơn vị, <span id="MathJax-Element-24-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>B</mi><mo>=</mo><mn>3</mn></math>"><span id="MJXc-Node-156" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-157" class="mjx-mrow"><span id="MJXc-Node-158" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">O</span></span><span id="MJXc-Node-159" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-160" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-161" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">3</span></span></span></span></span> đơn vị.</p>
<p>- Trên tia <span id="MathJax-Element-25-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>y</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>y</mi></math></span></span> đặt đoạn <span id="MathJax-Element-26-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><msup><mi>B</mi><mo>&#x2032;</mo></msup><mo>=</mo><mi>n</mi></math>"><span id="MJXc-Node-166" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-167" class="mjx-mrow"><span id="MJXc-Node-168" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">O</span></span><span id="MJXc-Node-169" class="mjx-msup"><span class="mjx-base"><span id="MJXc-Node-170" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span></span><span class="mjx-sup"><span id="MJXc-Node-171" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">′</span></span></span></span><span id="MJXc-Node-172" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-173" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">n</span></span></span></span></span></p>
<p>- Nối <span id="MathJax-Element-27-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><msup><mi>B</mi><mo>&#x2032;</mo></msup></math>"><span id="MJXc-Node-174" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-175" class="mjx-mrow"><span id="MJXc-Node-176" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-177" class="mjx-msup"><span class="mjx-base"><span id="MJXc-Node-178" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span></span><span class="mjx-sup"><span id="MJXc-Node-179" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">′</span></span></span></span></span></span></span></p>
<p>- Vẽ đường thẳng qua <span id="MathJax-Element-28-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math>"><span id="MJXc-Node-180" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-181" class="mjx-mrow"><span id="MJXc-Node-182" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span></span></span></span> song song với <span id="MathJax-Element-29-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><msup><mi>B</mi><mo>&#x2032;</mo></msup></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><msup><mi>B</mi><mo>′</mo></msup></math></span></span> cắt <span id="MathJax-Element-30-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>y</mi></math>"><span id="MJXc-Node-189" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-190" class="mjx-mrow"><span id="MJXc-Node-191" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">O</span></span><span id="MJXc-Node-192" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">y</span></span></span></span></span> tại <span id="MathJax-Element-31-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>A</mi><mo>&#x2032;</mo></msup></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>A</mi><mo>′</mo></msup></math></span></span> và đặt <span id="MathJax-Element-32-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><msup><mi>A</mi><mo>&#x2032;</mo></msup><mo>=</mo><mi>x</mi></math>"><span id="MJXc-Node-198" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-199" class="mjx-mrow"><span id="MJXc-Node-200" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">O</span></span><span id="MJXc-Node-201" class="mjx-msup"><span class="mjx-base"><span id="MJXc-Node-202" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span></span><span class="mjx-sup"><span id="MJXc-Node-203" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">′</span></span></span></span><span id="MJXc-Node-204" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-205" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">x</span></span></span></span></span>.</p>
<p>Khi đó OA' là đoạn thẳng cần dựng.</p>
<p>Chứng minh:</p>
<p>Xét tam giác OBB' có: <span id="MathJax-Element-33-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><msup><mi>A</mi><mo>&#x2032;</mo></msup><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>B</mi><msup><mi>B</mi><mo>&#x2032;</mo></msup></math>"><span id="MJXc-Node-206" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-207" class="mjx-mrow"><span id="MJXc-Node-208" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-209" class="mjx-msup"><span class="mjx-base"><span id="MJXc-Node-210" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span></span><span class="mjx-sup"><span id="MJXc-Node-211" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">′</span></span></span></span><span id="MJXc-Node-212" class="mjx-texatom"><span id="MJXc-Node-213" class="mjx-mrow"><span id="MJXc-Node-214" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-215" class="mjx-texatom"><span id="MJXc-Node-216" class="mjx-mrow"><span id="MJXc-Node-217" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-218" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-219" class="mjx-msup"><span class="mjx-base"><span id="MJXc-Node-220" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span></span><span class="mjx-sup"><span id="MJXc-Node-221" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">′</span></span></span></span></span></span></span></p>
<p><span class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><msup><mi>A</mi><mo>&#x2032;</mo></msup><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>B</mi><msup><mi>B</mi><mo>&#x2032;</mo></msup></math>"><span class="mjx-math" aria-hidden="true"><span class="mjx-mrow"><span class="mjx-msup"><span class="mjx-sup"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mfrac><mrow><mi>O</mi><mo>⁢</mo><msup><mi>A</mi><mo>'</mo></msup></mrow><mrow><mi>O</mi><mo>⁢</mo><msup><mi>B</mi><mo>'</mo></msup></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>O</mi><mo>⁢</mo><mi>A</mi></mrow><mrow><mi>O</mi><mo>⁢</mo><mi>B</mi></mrow></mfrac><mo>⁢</mo></math> (theo hệ quả định lí Talet)<br /></span></span></span></span></span></span></span></p>
<p><span class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><msup><mi>A</mi><mo>&#x2032;</mo></msup><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>B</mi><msup><mi>B</mi><mo>&#x2032;</mo></msup></math>"><span class="mjx-math" aria-hidden="true"><span class="mjx-mrow"><span class="mjx-msup"><span class="mjx-sup"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">hay <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mfrac><mi>x</mi><mi>n</mi></mfrac><mo>=</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></mstyle></math><br /></span></span></span></span></span></span></span></p>
<p><span class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><msup><mi>A</mi><mo>&#x2032;</mo></msup><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>B</mi><msup><mi>B</mi><mo>&#x2032;</mo></msup></math>"><span class="mjx-math" aria-hidden="true"><span class="mjx-mrow"><span class="mjx-msup"><span class="mjx-sup"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"><img src="https://img.loigiaihay.com/picture/2019/0313/bai-14b-trang-64-sgk-toan-8-t2.jpg" /></span></span></span></span></span></span></span></p>
<p><span class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><msup><mi>A</mi><mo>&#x2032;</mo></msup><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>B</mi><msup><mi>B</mi><mo>&#x2032;</mo></msup></math>"><span class="mjx-math" aria-hidden="true"><span class="mjx-mrow"><span class="mjx-msup"><span class="mjx-sup"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"><strong>LG c. </strong></span></span></span></span></span></span></span></p>
<p><span class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><msup><mi>A</mi><mo>&#x2032;</mo></msup><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>B</mi><msup><mi>B</mi><mo>&#x2032;</mo></msup></math>"><span class="mjx-math" aria-hidden="true"><span class="mjx-mrow"><span class="mjx-msup"><span class="mjx-sup"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mfrac><mi>m</mi><mi>x</mi></mfrac><mo>=</mo><mfrac><mi>n</mi><mi>p</mi></mfrac></mstyle></math></strong></span></span></span></span></span></span></span></p>
<p><strong>Phương pháp giải:</strong></p>
<p>Áp dụng hệ quả của định lý TaLet.</p>
<p><strong>Giải chi tiết:</strong></p>
<p>Cách dựng:</p>
<p>- Vẽ tia <span id="MathJax-Element-37-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>x</mi><mo>,</mo><mi>O</mi><mi>y</mi></math>"><span id="MJXc-Node-274" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-275" class="mjx-mrow"><span id="MJXc-Node-276" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">O</span></span><span id="MJXc-Node-277" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span><span id="MJXc-Node-278" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-279" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">O</span></span></span></span><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math></span></span> không đối nhau.</p>
<p>- Trên tia <span id="MathJax-Element-38-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>x</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>x</mi></math></span></span> đặt đoạn <span id="MathJax-Element-39-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>A</mi><mo>=</mo><mi>m</mi><mo>,</mo><mi>O</mi><mi>B</mi><mo>=</mo><mi>n</mi></math>"><span id="MJXc-Node-285" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-286" class="mjx-mrow"><span id="MJXc-Node-287" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">O</span></span><span id="MJXc-Node-288" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-289" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-290" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">m</span></span><span id="MJXc-Node-291" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-292" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">O</span></span><span id="MJXc-Node-293" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-294" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-295" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">n</span></span></span></span></span>.</p>
<p>- Trên tia <span id="MathJax-Element-40-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>y</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>y</mi></math></span></span> đặt đoạn <span id="MathJax-Element-41-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><msup><mi>B</mi><mo>&#x2032;</mo></msup><mo>=</mo><mi>p</mi></math>"><span id="MJXc-Node-300" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-301" class="mjx-mrow"><span id="MJXc-Node-302" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">O</span></span><span id="MJXc-Node-303" class="mjx-msup"><span class="mjx-base"><span id="MJXc-Node-304" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span></span><span class="mjx-sup"><span id="MJXc-Node-305" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">′</span></span></span></span><span id="MJXc-Node-306" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-307" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">p</span></span></span></span></span>.</p>
<p>- Vẽ đường thẳng qua <span id="MathJax-Element-42-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math>"><span id="MJXc-Node-308" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-309" class="mjx-mrow"><span id="MJXc-Node-310" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span></span></span></span> và song song với <span id="MathJax-Element-43-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><msup><mi>B</mi><mo>&#x2032;</mo></msup></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><msup><mi>B</mi><mo>′</mo></msup></math></span></span> cắt <span id="MathJax-Element-44-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>y</mi></math>"><span id="MJXc-Node-317" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-318" class="mjx-mrow"><span id="MJXc-Node-319" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">O</span></span><span id="MJXc-Node-320" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">y</span></span></span></span></span> tại <span id="MathJax-Element-45-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>A</mi><mo>&#x2032;</mo></msup></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>A</mi><mo>′</mo></msup></math></span></span> thì <span id="MathJax-Element-46-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><msup><mi>A</mi><mo>&#x2032;</mo></msup><mo>=</mo><mi>x</mi></math>"><span id="MJXc-Node-326" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-327" class="mjx-mrow"><span id="MJXc-Node-328" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">O</span></span><span id="MJXc-Node-329" class="mjx-msup"><span class="mjx-base"><span id="MJXc-Node-330" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span></span><span class="mjx-sup"><span id="MJXc-Node-331" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">′</span></span></span></span><span id="MJXc-Node-332" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-333" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">x</span></span></span></span></span> là đoạn thẳng cần dựng.</p>
<p>Chứng minh:</p>
<p>Xét tam giác OBB' có <span id="MathJax-Element-47-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><msup><mi>A</mi><mo>&#x2032;</mo></msup><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>B</mi><msup><mi>B</mi><mo>&#x2032;</mo></msup></math>"><span id="MJXc-Node-334" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-335" class="mjx-mrow"><span id="MJXc-Node-336" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-337" class="mjx-msup"><span class="mjx-base"><span id="MJXc-Node-338" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span></span><span class="mjx-sup"><span id="MJXc-Node-339" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">′</span></span></span></span><span id="MJXc-Node-340" class="mjx-texatom"><span id="MJXc-Node-341" class="mjx-mrow"><span id="MJXc-Node-342" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-343" class="mjx-texatom"><span id="MJXc-Node-344" class="mjx-mrow"><span id="MJXc-Node-345" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/BB'</span></span></span></span></span></span></span></p>
<p><span id="MathJax-Element-47-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><msup><mi>A</mi><mo>&#x2032;</mo></msup><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>B</mi><msup><mi>B</mi><mo>&#x2032;</mo></msup></math>"><span id="MJXc-Node-334" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-335" class="mjx-mrow"><span id="MJXc-Node-343" class="mjx-texatom"><span id="MJXc-Node-344" class="mjx-mrow"><span id="MJXc-Node-345" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>⇒</mo><mfrac><mrow><mi>O</mi><mo>⁢</mo><mi>A</mi></mrow><mrow><mi>O</mi><mo>⁢</mo><msup><mi>A</mi><mo>'</mo></msup></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>O</mi><mo>⁢</mo><mi>B</mi></mrow><mrow><mi>O</mi><mo>⁢</mo><msup><mi>B</mi><mo>'</mo></msup></mrow></mfrac></mstyle></math> (theo hệ quả định lí Talet) hay <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mfrac><mi>m</mi><mi>x</mi></mfrac><mo>=</mo><mfrac><mi>n</mi><mi>p</mi></mfrac></mstyle></math></span></span></span></span></span></span></span></p>
<p><span class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><msup><mi>A</mi><mo>&#x2032;</mo></msup><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>B</mi><msup><mi>B</mi><mo>&#x2032;</mo></msup></math>"><span class="mjx-math" aria-hidden="true"><span class="mjx-mrow"><span class="mjx-texatom"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"><img src="https://img.loigiaihay.com/picture/2019/0313/bai-14c-trang-64-sgk-toan-8-t2.jpg" /></span></span></span></span></span></span></span></p>
<p> </p>
<p> </p>
<p> </p>
<p> </p>
<p> </p>
<p> </p>
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