Bài 1: Định Lí Ta – Lét Trong Tam Giác
Hướng dẫn giải Bài 1 (Trang 58 SGK Toán Hình học 8, Tập 2)
<p><strong>LG a.</strong></p>
<p><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><mo>=</mo><mn>5</mn><mi>c</mi><mi>m</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-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-6" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">5</span></span><span id="MJXc-Node-7" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">c</span></span><span id="MJXc-Node-8" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">m</span></span></span></span></span> và <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>C</mi><mi>D</mi><mo>=</mo><mn>15</mn><mi>c</mi><mi>m</mi></math>"><span id="MJXc-Node-9" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-10" class="mjx-mrow"><span id="MJXc-Node-11" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-12" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span><span id="MJXc-Node-13" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-14" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">15</span></span><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-mi"><span class="mjx-char MJXc-TeX-math-I">m</span></span></span></span></span>;</p>
<p><strong>Phương pháp giải:</strong></p>
<p>Áp dụng định nghĩa: Tỉ số của hai đoạn thẳng là tỉ số độ dài của chúng theo cùng một đơn vị đo.</p>
<p>Tỉ số của a và b là <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mfrac><mi>a</mi><mi>b</mi></mfrac></mstyle></math><br /><strong>Lời giải chi tiết:</strong></p>
<p>Ta có <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: 400; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: 0px; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; color: #000000; font-family: OpenSans, Tahoma, Helvetica, sans-serif; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; 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></math>"><span id="MJXc-Node-24" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-25" class="mjx-mrow"><span id="MJXc-Node-26" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-27" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-28" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-29" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">5</span></span><span id="MJXc-Node-30" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">c</span></span><span id="MJXc-Node-31" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">m</span></span></span></span></span> và <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: 400; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: 0px; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; color: #000000; font-family: OpenSans, Tahoma, Helvetica, sans-serif; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mi>D</mi><mo>=</mo><mn>15</mn><mi>c</mi><mi>m</mi></math>"><span id="MJXc-Node-32" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-33" class="mjx-mrow"><span id="MJXc-Node-34" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-35" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span><span id="MJXc-Node-36" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-37" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">15</span></span><span id="MJXc-Node-38" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">c</span></span><span id="MJXc-Node-39" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">m</span></span></span></span></span><br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mfrac><mrow><mi>A</mi><mo></mo><mi>B</mi></mrow><mrow><mi>C</mi><mo></mo><mi>D</mi></mrow></mfrac><mo>=</mo><mfrac><mn>5</mn><mn>15</mn></mfrac><mo>=</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo></mo></math><br /><strong>LG b.</strong><br />EF=48cm và GH=16dm;<br /><strong>Phương pháp giải:</strong><br />Áp dụng định nghĩa: Tỉ số của hai đoạn thẳng là tỉ số độ dài của chúng theo cùng một đơn vị đo.<br />Tỉ số của a và b là <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mfrac><mi>a</mi><mi>b</mi></mfrac></mstyle></math><br /><strong>Lời giải chi tiết:</strong></p>
<p><span id="MJXc-Node-89" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-90" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span><span id="MJXc-Node-91" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-92" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">48</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-mi"><span class="mjx-char MJXc-TeX-math-I">m</span></span><span id="MJXc-Node-95" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-96" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">G</span></span><span id="MJXc-Node-97" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">H</span></span><span id="MJXc-Node-98" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-99" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">16</span></span><span id="MJXc-Node-100" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">d</span></span><span id="MJXc-Node-101" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">m</span></span><span id="MJXc-Node-102" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-103" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">160</span></span><span id="MJXc-Node-104" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">c</span></span><span id="MJXc-Node-105" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">m</span></span><br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mfrac><mrow><mi>E</mi><mo></mo><mi>F</mi></mrow><mrow><mi>G</mi><mo></mo><mi>H</mi></mrow></mfrac><mo>=</mo><mfrac><mn>48</mn><mn>160</mn></mfrac><mo>=</mo><mfrac><mn>3</mn><mn>10</mn></mfrac><mo></mo></math><br /><strong>LG c.</strong><br /><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: 400; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: 0px; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; color: #000000; font-family: OpenSans, Tahoma, Helvetica, sans-serif; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>Q</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mi>m</mi></math>"><span id="MJXc-Node-130" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-131" class="mjx-mrow"><span id="MJXc-Node-132" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">P</span></span><span id="MJXc-Node-133" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">Q</span></span><span id="MJXc-Node-134" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-135" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">1</span></span><span id="MJXc-Node-136" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-137" class="mjx-mn MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">2</span></span><span id="MJXc-Node-138" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">m</span></span></span></span></span> và <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: 400; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: 0px; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; color: #000000; font-family: OpenSans, Tahoma, Helvetica, sans-serif; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mi>N</mi><mo>=</mo><mn>24</mn><mi>c</mi><mi>m</mi></math>"><span id="MJXc-Node-139" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-140" class="mjx-mrow"><span id="MJXc-Node-141" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">M</span></span><span id="MJXc-Node-142" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">N</span></span><span id="MJXc-Node-143" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-144" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">24</span></span><span id="MJXc-Node-145" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">c</span></span><span id="MJXc-Node-146" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">m</span></span></span></span></span>.</p>
<p><strong>Phương pháp giải:</strong></p>
<p>Áp dụng định nghĩa: Tỉ số của hai đoạn thẳng là tỉ số độ dài của chúng theo cùng một đơn vị đo.</p>
<p>Tỉ số của a và b là <math xmlns="http://www.w3.org/1998/Math/MathML"><mo></mo><mfrac><mi>a</mi><mi>b</mi></mfrac><mo></mo></math></p>
<p><strong>Lời giải chi tiết:</strong></p>
<p><span id="MJXc-Node-156" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">P</span></span><span id="MJXc-Node-157" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">Q</span></span><span id="MJXc-Node-158" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-159" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">1</span></span><span id="MJXc-Node-160" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-161" class="mjx-mn MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">2</span></span><span id="MJXc-Node-162" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">m</span></span><span id="MJXc-Node-163" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-164" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">120</span></span><span id="MJXc-Node-165" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">c</span></span><span id="MJXc-Node-166" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">m</span></span><span id="MJXc-Node-167" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-168" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">M</span></span><span id="MJXc-Node-169" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">N</span></span><span id="MJXc-Node-170" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-171" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">24</span></span><span id="MJXc-Node-172" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">c</span></span><span id="MJXc-Node-173" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">m</span></span><br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mfrac><mrow><mi>P</mi><mo></mo><mi>Q</mi></mrow><mrow><mi>M</mi><mo></mo><mi>N</mi></mrow></mfrac><mo>=</mo><mfrac><mn>120</mn><mn>24</mn></mfrac><mo>=</mo><mn>5</mn><mo>.</mo></math><br /><br /></p>
<p> </p>
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