Bài 10: Đường Thẳng Song Song Với Một Đường Thẳng Cho Trước
Hướng dẫn giải Bài 67 (Trang 102 SGK Toán Hình học 8, Tập 1)
<p><strong class="content_question">Đề bài</strong></p>
<p>Cho đoạn thẳng <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>A</mi><mi>B</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">A</span></span><span id="MJXc-Node-4" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span></span></span></span>. Kẻ tia <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>x</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>x</mi></math></span></span> bất kì. Trên tia <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"><mi>A</mi><mi>x</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>x</mi></math></span></span> lấy các điểm <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>C</mi><mo>,</mo><mi>D</mi><mo>,</mo><mi>E</mi></math>"><span id="MJXc-Node-13" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-14" class="mjx-mrow"><span id="MJXc-Node-15" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-16" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-17" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">D</span></span><span id="MJXc-Node-18" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-19" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">E</span></span></span></span></span> sao cho <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>A</mi><mi>C</mi><mo>=</mo><mi>C</mi><mi>D</mi><mo>=</mo><mi>D</mi><mi>E</mi></math>"><span id="MJXc-Node-20" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-21" class="mjx-mrow"><span id="MJXc-Node-22" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-23" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-24" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-25" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-26" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span><span id="MJXc-Node-27" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-28" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">D</span></span><span id="MJXc-Node-29" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span></span></span></span> (h.97). Kẻ 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>E</mi><mi>B</mi></math>"><span id="MJXc-Node-30" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-31" class="mjx-mrow"><span id="MJXc-Node-32" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span></span></span><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math></span></span>. Qua <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>C</mi><mo>,</mo><mi>D</mi></math>"><span id="MJXc-Node-34" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-35" class="mjx-mrow"><span id="MJXc-Node-36" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-37" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-38" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">D</span></span></span></span></span> kẻ các đường thẳng song song với <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>B</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>B</mi></math></span></span>. Chứng minh rằng đoạn thẳng <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 id="MJXc-Node-43" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-44" class="mjx-mrow"><span id="MJXc-Node-45" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-46" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span></span></span></span> bị chia ra ba phần bằng nhau.</p>
<p><strong class="content_detail">Lời giải chi tiết</strong></p>
<p><img class="wscnph" style="max-width: 100%;" src="https://static.colearn.vn:8413/v1.0/upload/library/05072022/b67-trand-102-sdk-toan-8-t-1-c2-RzzORY.jpg" /></p>
<p>Qua <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>A</mi></math>"><span id="MJXc-Node-47" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-48" class="mjx-mrow"><span id="MJXc-Node-49" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span></span></span></span> dựng đường thẳng <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 id="MJXc-Node-50" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-51" class="mjx-mrow"><span id="MJXc-Node-52" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">d</span></span></span></span></span> 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>C</mi><msup><mi>C</mi><mo>&#x2032;</mo></msup></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><msup><mi>C</mi><mo>′</mo></msup></math></span></span></p>
<p>Ta có: <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>d</mi><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>E</mi><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>D</mi><msup><mi>D</mi><mo>&#x2032;</mo></msup><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>C</mi><msup><mi>C</mi><mo>&#x2032;</mo></msup></math>"><span id="MJXc-Node-59" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-60" class="mjx-mrow"><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-texatom"><span id="MJXc-Node-63" class="mjx-mrow"><span id="MJXc-Node-64" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-65" class="mjx-texatom"><span id="MJXc-Node-66" class="mjx-mrow"><span id="MJXc-Node-67" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-68" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-69" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-70" class="mjx-texatom"><span id="MJXc-Node-71" class="mjx-mrow"><span id="MJXc-Node-72" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-73" class="mjx-texatom"><span id="MJXc-Node-74" class="mjx-mrow"><span id="MJXc-Node-75" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-76" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span><span id="MJXc-Node-77" class="mjx-msup"><span class="mjx-base"><span id="MJXc-Node-78" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span></span><span class="mjx-sup"><span id="MJXc-Node-79" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">′</span></span></span></span><span id="MJXc-Node-80" class="mjx-texatom"><span id="MJXc-Node-81" class="mjx-mrow"><span id="MJXc-Node-82" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-83" class="mjx-texatom"><span id="MJXc-Node-84" class="mjx-mrow"><span id="MJXc-Node-85" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-86" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-87" class="mjx-msup"><span class="mjx-base"><span id="MJXc-Node-88" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span></span><span class="mjx-sup"><span id="MJXc-Node-89" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">′</span></span></span></span></span></span></span> và <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>A</mi><mi>C</mi><mo>=</mo><mi>C</mi><mi>D</mi><mo>=</mo><mi>D</mi><mi>E</mi></math>"><span id="MJXc-Node-90" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-91" class="mjx-mrow"><span id="MJXc-Node-92" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-93" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-94" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-95" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-96" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span><span id="MJXc-Node-97" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-98" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">D</span></span><span id="MJXc-Node-99" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span></span></span></span> (theo giả thiết).</p>
<p>Theo định lí về các đường thẳng song song cách đều ta suy ra các đường thẳng <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>d</mi><mo>,</mo><mi>E</mi><mi>B</mi><mo>,</mo><mi>D</mi><msup><mi>D</mi><mo>&#x2032;</mo></msup><mo>,</mo><mi>C</mi><msup><mi>C</mi><mo>&#x2032;</mo></msup></math>"><span id="MJXc-Node-100" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-101" class="mjx-mrow"><span id="MJXc-Node-102" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">d</span></span><span id="MJXc-Node-103" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-104" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-105" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-106" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-107" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">D</span></span><span id="MJXc-Node-108" class="mjx-msup"><span class="mjx-base"><span id="MJXc-Node-109" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span></span><span class="mjx-sup"><span id="MJXc-Node-110" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">′</span></span></span></span><span id="MJXc-Node-111" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-112" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-113" class="mjx-msup"><span class="mjx-base"><span id="MJXc-Node-114" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span></span><span class="mjx-sup"><span id="MJXc-Node-115" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">′</span></span></span></span></span></span></span> là các đường thẳng song song cách đều nên nó chắn trên <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>A</mi><mi>B</mi></math>"><span id="MJXc-Node-116" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-117" class="mjx-mrow"><span id="MJXc-Node-118" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span></span></span><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math></span></span> các đoạn thẳng liên tiếp bằng nhau</p>
<p>Hay <span id="MathJax-Element-17-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>C</mi><mo>&#x2032;</mo></msup><mo>=</mo><msup><mi>C</mi><mo>&#x2032;</mo></msup><msup><mi>D</mi><mo>&#x2032;</mo></msup><mo>=</mo><msup><mi>D</mi><mo>&#x2032;</mo></msup><mi>B</mi></math>"><span id="MJXc-Node-120" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-121" class="mjx-mrow"><span id="MJXc-Node-122" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-123" class="mjx-msup"><span class="mjx-base"><span id="MJXc-Node-124" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span></span><span class="mjx-sup"><span id="MJXc-Node-125" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">′</span></span></span></span><span id="MJXc-Node-126" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-127" class="mjx-msup MJXc-space3"><span class="mjx-base"><span id="MJXc-Node-128" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span></span><span class="mjx-sup"><span id="MJXc-Node-129" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">′</span></span></span></span><span id="MJXc-Node-130" class="mjx-msup"><span class="mjx-base"><span id="MJXc-Node-131" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span></span><span class="mjx-sup"><span id="MJXc-Node-132" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">′</span></span></span></span><span id="MJXc-Node-133" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-134" class="mjx-msup MJXc-space3"><span class="mjx-base"><span id="MJXc-Node-135" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span></span><span class="mjx-sup"><span id="MJXc-Node-136" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">′</span></span></span></span><span id="MJXc-Node-137" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span></span></span></span></p>
<p>Vậy đoạn thẳng <span id="MathJax-Element-18-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-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">A</span></span></span></span><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math></span></span> bị chia thành ba phần bằng nhau.</p>
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