Bài 3: Tính Chất Đường Phân Giác Của Tam Giác
Hướng dẫn giải Bài 18 (Trang 68 SGK Toán Hình học 8, Tập 2)
<p><strong class="content_question">Đề bài</strong></p>
<p>Tam giác <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><mi>C</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 id="MJXc-Node-5" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span></span></span></span> có <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><mn>5</mn><mi>c</mi><mi>m</mi><mo>,</mo><mi>A</mi><mi>C</mi><mo>=</mo><mn>6</mn><mi>c</mi><mi>m</mi><mo>,</mo><mi>B</mi><mi>C</mi><mo>=</mo><mn>7</mn><mi>c</mi><mi>m</mi><mo>.</mo></math>"><span id="MJXc-Node-6" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-7" class="mjx-mrow"><span id="MJXc-Node-8" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-9" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-10" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-11" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">5</span></span><span id="MJXc-Node-12" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">c</span></span><span id="MJXc-Node-13" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">m</span></span><span id="MJXc-Node-14" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-15" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-16" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-17" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-18" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">6</span></span><span id="MJXc-Node-19" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">c</span></span><span id="MJXc-Node-20" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">m</span></span><span id="MJXc-Node-21" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-22" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">B</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-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">7</span></span><span id="MJXc-Node-26" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">c</span></span><span id="MJXc-Node-27" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">m</span></span><span id="MJXc-Node-28" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">.</span></span></span></span></span> Tia phân giác của góc <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>B</mi><mi>A</mi><mi>C</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mi>A</mi><mi>C</mi></math></span></span> cắt <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>B</mi><mi>C</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mi>C</mi></math></span></span> tại <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>E</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi></math></span></span>. Tính các đoạn <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><mo>,</mo><mi>E</mi><mi>C</mi></math>"><span id="MJXc-Node-41" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-42" class="mjx-mrow"><span id="MJXc-Node-43" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-44" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-45" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-46" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-47" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span></span></span></span>.</p>
<p><strong class="content_detail">Lời giải chi tiết</strong></p>
<p><span class="content_detail">Vì AE là đường phân giác của tam giác <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi>ABC</mi></mstyle></math> nên<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mfrac><mrow><mi>E</mi><mo>⁢</mo><mi>B</mi></mrow><mrow><mi>A</mi><mo>⁢</mo><mi>B</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>E</mi><mo>⁢</mo><mi>C</mi></mrow><mrow><mi>A</mi><mo>⁢</mo><mi>C</mi></mrow></mfrac></mstyle></math> (tính chất đường phân giác của tam giác)<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mfrac><mrow><mi>E</mi><mo>⁢</mo><mi>B</mi></mrow><mn>5</mn></mfrac><mo>=</mo><mfrac><mrow><mi>E</mi><mo>⁢</mo><mi>C</mi></mrow><mn>6</mn></mfrac><mo>⁢</mo></math><br />Áp dụng tính chất của dãy tỉ số bằng nhau ta có:<br /></span><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⁢</mo><mfrac><mrow><mi>E</mi><mo>⁢</mo><mi>B</mi></mrow><mn>5</mn></mfrac><mo>=</mo><mfrac><mrow><mi>E</mi><mo>⁢</mo><mi>C</mi></mrow><mn>6</mn></mfrac><mo>=</mo><mfrac><mrow><mi>E</mi><mo>⁢</mo><mi>B</mi><mo>+</mo><mi>E</mi><mo>⁢</mo><mi>C</mi></mrow><mrow><mn>5</mn><mo>+</mo><mn>6</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>B</mi><mo>⁢</mo><mi>C</mi></mrow><mn>11</mn></mfrac><mo>=</mo><mpadded><mfrac><mn>7</mn><mn>11</mn></mfrac></mpadded><mo>⁢</mo><mspace linebreak="newline"/><mo>⇒</mo><mi>E</mi><mo>⁢</mo><mi>B</mi><mo>=</mo><mfrac><mn>5.7</mn><mn>11</mn></mfrac><mo>=</mo><mpadded><mfrac><mn>35</mn><mn>11</mn></mfrac></mpadded><mo>⁢</mo><mpadded><mi>cm</mi></mpadded><mo>⁢</mo><mspace linebreak="newline"/><mo>⁢</mo><mi>E</mi><mo>⁢</mo><mi>C</mi><mo>=</mo><mfrac><mn>6.7</mn><mn>11</mn></mfrac><mo>=</mo><mpadded><mfrac><mn>42</mn><mn>11</mn></mfrac></mpadded><mo>⁢</mo><mi>cm</mi></math><strong class="content_detail"><br /></strong></p>
<p> </p>
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