Bài 2: Định Lí Đảo Và Hệ Quả Của Định Lí Ta-Lét
Hướng dẫn giải Bài 8 (Trang 63 SGK Toán Hình học 8, Tập 2)
<p><img src="https://img.loigiaihay.com/picture/2018/0718/b8-trang-63-sgk-toan-8-t2-c2.jpg" /></p>
<p><strong>LG a.</strong></p>
<p>Để chia đoạn thẳng AB thành ba đoạn bằng nhau, người ta đã làm như hình 15.</p>
<p>Hãy mô tả cách làm trên và giải thích vì sao các đoạn AC, CD, DB bằng nhau?</p>
<p><strong>Phương pháp giải:</strong></p>
<p>Áp dụng: Hệ quả của định lý TaLet.</p>
<p><strong>Lời giải chi tiết:</strong></p>
<p>Mô tả cách làm:</p>
<p>Vẽ đoạn <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>P</mi><mi>Q</mi></math>"><span id="MJXc-Node-1" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-2" class="mjx-mrow"><span id="MJXc-Node-3" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">P</span></span><span id="MJXc-Node-4" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">Q</span></span></span></span></span> song song với <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>A</mi><mi>B</mi><mo>,</mo><mi>P</mi><mi>Q</mi></math>"><span id="MJXc-Node-5" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-6" class="mjx-mrow"><span id="MJXc-Node-7" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-8" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-9" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-10" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">P</span></span><span id="MJXc-Node-11" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">Q</span></span></span></span></span> có độ dài bằng <span id="MathJax-Element-3-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"><mn>3</mn></math>"><span id="MJXc-Node-12" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-13" class="mjx-mrow"><span id="MJXc-Node-14" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">3</span></span></span></span></span> đơn vị</p>
<p>- Trên PQ lấy lần lượt các điểm E, F sao cho <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>P</mi><mi>E</mi><mo>=</mo><mi>E</mi><mi>F</mi><mo>=</mo><mi>F</mi><mi>Q</mi><mo>=</mo><mn>1</mn></math>"><span id="MJXc-Node-15" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-16" class="mjx-mrow"><span id="MJXc-Node-17" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">P</span></span><span id="MJXc-Node-18" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-19" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-20" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-21" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span><span id="MJXc-Node-22" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-23" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">F</span></span><span id="MJXc-Node-24" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">Q</span></span><span id="MJXc-Node-25" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span></span></span><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></span></span> đơn vị </p>
<p>- Xác định giao điểm <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></math>"><span id="MJXc-Node-27" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-28" class="mjx-mrow"><span id="MJXc-Node-29" class="mjx-mi"><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>O</mi></math></span></span> của hai đoạn thẳng <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>P</mi><mi>B</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>B</mi></math></span></span> và <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>Q</mi><mi>A</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mi>A</mi></math></span></span>.</p>
<p>- Vẽ các đường thẳng <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>E</mi><mi>O</mi><mo>,</mo><mi>F</mi><mi>O</mi></math>"><span id="MJXc-Node-38" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-39" class="mjx-mrow"><span id="MJXc-Node-40" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-41" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">O</span></span><span id="MJXc-Node-42" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-43" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">F</span></span><span id="MJXc-Node-44" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">O</span></span></span></span></span> cắt <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>A</mi><mi>B</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>B</mi></math></span></span> tại <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>C</mi></math>"><span id="MJXc-Node-49" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-50" class="mjx-mrow"><span id="MJXc-Node-51" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span></span></span></span> và <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>D</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math></span></span>.</p>
<p>Chứng minh <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>A</mi><mi>C</mi><mo>=</mo><mi>C</mi><mi>D</mi><mo>=</mo><mi>D</mi><mi>B</mi></math>"><span id="MJXc-Node-55" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-56" class="mjx-mrow"><span id="MJXc-Node-57" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-58" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-59" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-60" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-61" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span><span id="MJXc-Node-62" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-63" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">D</span></span><span id="MJXc-Node-64" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span></span></span></span></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi mathvariant="normal">△</mi><mo>⁢</mo><mi>O</mi><mo>⁢</mo><mi>P</mi><mo>⁢</mo><mi>E</mi></mstyle></math> có PE//DB (theo cách vẽ) nên <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mfrac><mrow><mi>D</mi><mo>⁢</mo><mi>B</mi></mrow><mrow><mi>P</mi><mo>⁢</mo><mi>E</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>O</mi><mo>⁢</mo><mi>D</mi></mrow><mrow><mi>O</mi><mo>⁢</mo><mi>E</mi></mrow></mfrac></mstyle></math> (1) (hệ quả định lý TaLet)<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi mathvariant="normal">Δ</mi><mo>⁢</mo><mi>O</mi><mo>⁢</mo><mi>E</mi><mo>⁢</mo><mi>F</mi></mstyle></math> và <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi mathvariant="normal">△</mi><mo>⁢</mo><mi>O</mi><mo>⁢</mo><mi>D</mi><mo>⁢</mo><mi>C</mi></mstyle></math> có EF//CD (theo cách vẽ) nên <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mfrac><mrow><mi>C</mi><mo>⁢</mo><mi>D</mi></mrow><mrow><mi>E</mi><mo>⁢</mo><mi>F</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>O</mi><mo>⁢</mo><mi>D</mi></mrow><mrow><mi>O</mi><mo>⁢</mo><mi>E</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>O</mi><mo>⁢</mo><mi>C</mi></mrow><mrow><mi>O</mi><mo>⁢</mo><mi>F</mi></mrow></mfrac></mstyle></math> (2) (hệ quả định lý TaLet)<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi mathvariant="normal">△</mi><mo>⁢</mo><mi>O</mi><mo>⁢</mo><mi>F</mi><mo>⁢</mo><mi>Q</mi></mstyle></math> và <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi mathvariant="normal">△</mi><mo>⁢</mo><mi>O</mi><mo>⁢</mo><mi>C</mi><mo>⁢</mo><mi>A</mi></mstyle></math> có FQ//AC (theo cách vẽ) nên <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mfrac><mrow><mi>A</mi><mo>⁢</mo><mi>C</mi></mrow><mrow><mi>F</mi><mo>⁢</mo><mi>Q</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>O</mi><mo>⁢</mo><mi>C</mi></mrow><mrow><mi>O</mi><mo>⁢</mo><mi>F</mi></mrow></mfrac></mstyle></math> (3) (hệ quả định lý TaLet)<br />Từ' (1), (2) và (3) suy ra:<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mfrac><mrow><mi>D</mi><mo>⁢</mo><mi>B</mi></mrow><mrow><mi>P</mi><mo>⁢</mo><mi>E</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>C</mi><mo>⁢</mo><mi>D</mi></mrow><mrow><mi>E</mi><mo>⁢</mo><mi>F</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>A</mi><mo>⁢</mo><mi>C</mi></mrow><mrow><mi>F</mi><mo>⁢</mo><mi>Q</mi></mrow></mfrac></mstyle></math> mà PE=EF=FQ (gt) nên DB=CD=AC.<br />Vây: DB=CD=AC.</p>
<p><strong>LG b.</strong></p>
<p>Bằng cách tương tự, hãy chia đoạn thẳng AB cho trước thành 5 đoạn bằng nhau. Hỏi có cách nào khác với cách làm trên mà vẫn có thể chia đoạn AB cho trước thành 5 đoạn bằng nhau?</p>
<p><strong>Phương pháp giải:</strong></p>
<p>Áp dụng: Hệ quả của định lý TaLet.</p>
<p><strong>Lời giải chi tiết:</strong></p>
<p>Tương tự chia đoạn thẳng <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>A</mi><mi>B</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>B</mi></math></span></span> thành <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"><mn>5</mn></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></span></span> đoạn bằng nhau thực hiện như hình vẽ sau:\</p>
<p><img src="https://img.loigiaihay.com/picture/2019/0313/bai-81-trang-63-sgk-toan-8-t2.jpg" /></p>
<p>Cách khác: Ta có thể chia đoạn thẳng <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"><mi>A</mi><mi>B</mi></math>"><span id="MJXc-Node-278" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-279" class="mjx-mrow"><span id="MJXc-Node-280" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-281" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span></span></span></span> thành <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"><mn>5</mn></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></span></span> đoạn thẳng bằng nhau như cách sau:</p>
<p>Vẽ <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"><mn>6</mn></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-mn"><span class="mjx-char MJXc-TeX-main-R">6</span></span></span></span></span> đường thẳng song song cách đều nhau (có thể dùng thước kẻ để vẽ liên tiếp). Đặt đầu mút <span id="MathJax-Element-34-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-288" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-289" class="mjx-mrow"><span id="MJXc-Node-290" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span></span></span></span> và <span id="MathJax-Element-35-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> ở hai đường thẳng ngoài cùng thì các đường thẳng song song cắt <span id="MathJax-Element-36-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><mi>B</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>B</mi></math></span></span> chia thành <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"><mn>5</mn></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></span></span> phần bằng nhau. </p>
<p><img src="https://img.loigiaihay.com/picture/2019/0313/bai-82-trang-63-sgk-toan-8-t2.jpg" /></p>
<p> </p>
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