Ôn tập chương 2
Hướng dẫn giải Bài 41 (Trang 132 SGK Toán Hình học 8, Tập 1)
<p><strong class="content_question">Đề bài</strong></p>
<p>Cho hình chữ nhật <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><mi>D</mi><mo>.</mo></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 id="MJXc-Node-6" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span></span></span><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>.</mo></math></span></span> Gọi <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>H</mi><mo>,</mo><mi>I</mi><mo>,</mo><mi>E</mi><mo>,</mo><mi>K</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">H</span></span><span id="MJXc-Node-11" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-12" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">I</span></span><span id="MJXc-Node-13" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-14" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-15" class="mjx-mo"><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"><mi>K</mi></math></span></span> lần lượt là các trung điểm của <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>C</mi><mo>,</mo><mi>H</mi><mi>C</mi><mo>,</mo><mi>D</mi><mi>C</mi><mo>,</mo><mi>E</mi><mi>C</mi></math>"><span id="MJXc-Node-17" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-18" class="mjx-mrow"><span id="MJXc-Node-19" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-20" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</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">H</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"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-25" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">D</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-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-28" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-29" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span></span></span></span> (h.<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"><mn>159</mn></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-mn"><span class="mjx-char MJXc-TeX-main-R">15</span></span></span></span><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></span></span>)</p>
<p>Tính:</p>
<p>a) Diện tích tam giác <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>D</mi><mi>B</mi><mi>E</mi><mo>;</mo></math>"><span id="MJXc-Node-33" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-34" class="mjx-mrow"><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-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-37" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-38" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">;</span></span></span></span></span></p>
<p>b) Diện tích tứ giác <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>H</mi><mi>I</mi><mi>K</mi><mo>.</mo></math>"><span id="MJXc-Node-39" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-40" class="mjx-mrow"><span id="MJXc-Node-41" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-42" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">H</span></span><span id="MJXc-Node-43" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">I</span></span><span id="MJXc-Node-44" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">K</span></span><span id="MJXc-Node-45" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">.</span></span></span></span></span></p>
<p><img src="https://img.loigiaihay.com/picture/2018/0716/b41-trang-132-sgk-toan-8-t-1-c2.jpg" /><br /><br /><br /></p>
<p>a) Ta có: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi>D</mi><mo>⁢</mo><mi>E</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⁢</mo><mi>D</mi><mo>⁢</mo><mi>C</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⋅</mo><mn>12</mn><mo>=</mo><mn>6</mn><mo>⁢</mo><mrow><mo>(</mo><mi>cm</mi><mo>)</mo></mrow></mstyle></math> (tính chất trung điểm)<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><msub><mi>S</mi><mrow><mi>D</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>E</mi></mrow></msub><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⋅</mo><mi>D</mi><mo>⁢</mo><mi>E</mi><mo>⋅</mo><mi>B</mi><mo>⁢</mo><mi>C</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⋅</mo><mn>6</mn><mo>⋅</mo><mn>6</mn><mo>,</mo><mn>8</mn><mo>=</mo><mn>20</mn><mo>,</mo><mn>4</mn><mo>⁢</mo><mrow><mo>(</mo><msup><mi>cm</mi><mn>2</mn></msup><mo>)</mo></mrow></mstyle></math><br />b) Ta có : <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi>H</mi><mo>⁢</mo><mi>C</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>C</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⋅</mo><mn>6</mn><mo>,</mo><mn>8</mn><mo>=</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>⁢</mo><mrow><mo>(</mo><mi>cm</mi><mo>)</mo></mrow></mstyle></math> (tính chất trung điểm)<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi>H</mi><mo>⁢</mo><mi>I</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⁢</mo><mi>H</mi><mo>⁢</mo><mi>C</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⋅</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>=</mo><mn>1</mn><mo>,</mo><mn>7</mn><mo>⁢</mo><mrow><mo>(</mo><mi>cm</mi><mo>)</mo></mrow></mstyle></math> (tính chất trung điểm)<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi>E</mi><mo>⁢</mo><mi>C</mi><mo>=</mo><mi>D</mi><mo>⁢</mo><mi>E</mi><mo>=</mo><mpadded><mn>6</mn></mpadded><mo>⁢</mo><mi>cm</mi></mstyle></math> (tính chất trung điểm)<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi>E</mi><mo>⁢</mo><mi>K</mi><mo>=</mo><mi>K</mi><mo>⁢</mo><mi>C</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⁢</mo><mi>E</mi><mo>⁢</mo><mi>C</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⋅</mo><mn>6</mn><mo>=</mo><mn>3</mn><mo>⁢</mo><mrow><mo>(</mo><mi>cm</mi><mo>)</mo></mrow></mstyle></math> (tính chất trung điểm)<br />Do đó<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><msub><mi>S</mi><mrow><mi>E</mi><mo>⁢</mo><mi>H</mi><mo>⁢</mo><mi>I</mi><mo>⁢</mo><mi>K</mi></mrow></msub><mo>=</mo><msub><mi>S</mi><mrow><mi>E</mi><mo>⁢</mo><mi>H</mi><mo>⁢</mo><mi>K</mi></mrow></msub><mo>+</mo><msub><mi>S</mi><mrow><mi>H</mi><mo>⁢</mo><mi>K</mi><mo>⁢</mo><mi>I</mi></mrow></msub></mstyle></math><br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⁢</mo><mi>E</mi><mo>⁢</mo><mi>K</mi><mo>.</mo><mi>H</mi><mo>⁢</mo><mi>C</mi><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⁢</mo><mi>H</mi><mo>⁢</mo><mi>I</mi><mo>.</mo><mi>K</mi><mo>⁢</mo><mi>C</mi></mstyle></math><br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⁢</mo><mi>E</mi><mo>⁢</mo><mi>K</mi><mo>.</mo><mi>H</mi><mo>⁢</mo><mi>C</mi><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⁢</mo><mi>E</mi><mo>⁢</mo><mi>K</mi><mo>.</mo><mi>H</mi><mo>⁢</mo><mi>I</mi></mstyle></math><br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⁢</mo><mi>E</mi><mo>⁢</mo><mi>K</mi><mo>⁢</mo><mrow><mo>(</mo><mi>H</mi><mo>⁢</mo><mi>C</mi><mo>+</mo><mi>H</mi><mo>⁢</mo><mi>I</mi><mo>)</mo></mrow></mstyle></math><br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><msub><mi>S</mi><mrow><mi>E</mi><mo>⁢</mo><mi>H</mi><mo>⁢</mo><mi>I</mi><mo>⁢</mo><mi>K</mi></mrow></msub><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⋅</mo><mn>3</mn><mo>⋅</mo><mrow><mo>(</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>+</mo><mn>1</mn><mo>,</mo><mn>7</mn><mo>)</mo></mrow><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⋅</mo><mn>3</mn><mo>⋅</mo><mn>5</mn><mo>,</mo><mn>1</mn><mo>=</mo><mn>7</mn><mo>,</mo><mn>65</mn><mo>⁢</mo><mrow><mo>(</mo><msup><mi>cm</mi><mn>2</mn></msup><mo>)</mo></mrow></mstyle></math></p>
<p>Cách khác:<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⁢</mo><msub><mi>S</mi><mrow><mi>E</mi><mo>⁢</mo><mi>H</mi><mo>⁢</mo><mi>I</mi><mo>⁢</mo><mi>K</mi></mrow></msub><mo>=</mo><msub><mi>S</mi><mrow><mi>E</mi><mo>⁢</mo><mi>H</mi><mo>⁢</mo><mi>C</mi></mrow></msub><mo>-</mo><msub><mi>S</mi><mrow><mi>K</mi><mo>⁢</mo><mi>I</mi><mo>⁢</mo><mi>C</mi></mrow></msub><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⁢</mo><mi>E</mi><mo>⁢</mo><mi>C</mi><mo>.</mo><mi>H</mi><mo>⁢</mo><mi>C</mi><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⁢</mo><mi>K</mi><mo>⁢</mo><mi>C</mi><mo>.</mo><mi>I</mi><mo>⁢</mo><mpadded><mi>C</mi></mpadded><mo>⁢</mo><mspace linebreak="newline"/><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⋅</mo><mn>6.3</mn><mo>,</mo><mn>4</mn><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⋅</mo><mn>3.1</mn><mo>,</mo><mpadded><mn>7</mn></mpadded><mo>⁢</mo><mspace linebreak="newline"/><mo>=</mo><mn>10</mn><mo>,</mo><mn>2</mn><mo>-</mo><mn>2</mn><mo>,</mo><mn>55</mn><mo>=</mo><mn>7</mn><mo>,</mo><mn>65</mn><mo>⁢</mo><mrow><mo>(</mo><msup><mi>cm</mi><mn>2</mn></msup><mo>)</mo></mrow></math></p>
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