Ôn tập chương 2
Hướng dẫn giải Bài 44 (Trang 133 SGK Toán Hình học 8, Tập 1)
<p><strong class="content_question">Đề bài</strong></p>
<p>Gọi <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>O</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">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> là điểm nằm trong hình bình hành <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><mi>C</mi><mi>D</mi><mo>.</mo></math>"><span class="MJX_Assistive_MathML" role="presentation"><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></span> Chứng minh rằng tổng diện tích của hai tam giác <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>B</mi><mi>O</mi></math>"><span id="MJXc-Node-11" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-12" class="mjx-mrow"><span id="MJXc-Node-13" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-14" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-15" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">O</span></span></span></span></span> và <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><mi>D</mi><mi>O</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mi>D</mi><mi>O</mi></math></span></span> bằng tổng diện tích của hai 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>B</mi><mi>C</mi><mi>O</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mi>C</mi><mi>O</mi></math></span></span> và <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>D</mi><mi>A</mi><mi>O</mi><mo>.</mo></math>"><span id="MJXc-Node-26" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-27" class="mjx-mrow"><span id="MJXc-Node-28" class="mjx-mi"><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">A</span></span><span id="MJXc-Node-30" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">O.</span></span><span id="MJXc-Node-31" class="mjx-mo"></span></span></span></span></p>
<p><strong><span 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-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>A</mi><mi>O</mi><mo>.</mo></math>"><span class="mjx-math" aria-hidden="true"><span class="mjx-mrow"><span class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">Lời giải chi tiết</span></span></span></span></span></strong></p>
<p><img src="https://img.loigiaihay.com/picture/2018/0716/b44-trang-133-sgk-toan-8-t-1-c2.jpg" /></p>
<p>Từ O kẻ đường thẳng d vuông góc với AB ở <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><msub><mi>H</mi><mn>1</mn></msub></mstyle></math>, cắt CD ở <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>H</mi><mn>2</mn></msub><mo>.</mo></math><br />Ta có <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi>O</mi><mo>⁢</mo><msub><mi>H</mi><mn>1</mn></msub><mo>⟂</mo><mi>A</mi><mo>⁢</mo><mi>B</mi></mstyle></math> (theo cách vẽ)<br />Mà AB//CD (vì ABCD là hình bình hành)<br />Nên <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><msub><mi>OH</mi><mn>2</mn></msub><mo>⟂</mo><mi>CD</mi></mstyle></math><br />Do đó <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><msub><mi>S</mi><mrow><mi>A</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>O</mi></mrow></msub><mo>+</mo><msub><mi>S</mi><mrow><mi>C</mi><mo>⁢</mo><mi>D</mi><mo>⁢</mo><mi>O</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>O</mi><mo>⁢</mo><msub><mi>H</mi><mn>1</mn></msub><mo>⋅</mo><mi>A</mi><mo>⁢</mo><mi>B</mi><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⁢</mo><mi>O</mi><mo>⁢</mo><msub><mi>H</mi><mn>2</mn></msub><mo>⋅</mo><mi>C</mi><mo>⁢</mo><mi>D</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><mi>O</mi><msub><mi>H</mi><mn>1</mn></msub><mo>⋅</mo><mi>A</mi><mi>B</mi><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>O</mi><msub><mi>H</mi><mn>2</mn></msub><mo>⋅</mo><mi>A</mi><mi>B</mi></mstyle></math> (vì AB=CD)<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>AB</mi><mo>⁢</mo><mrow><mo>(</mo><msub><mi>OH</mi><mn>1</mn></msub><mo>+</mo><msub><mi>OH</mi><mn>2</mn></msub><mo>)</mo></mrow></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>A</mi><mo>⁢</mo><mi>B</mi><mo>⋅</mo><msub><mi>H</mi><mn>1</mn></msub><mo>⁢</mo><msub><mi>H</mi><mn>2</mn></msub></mstyle></math><br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mrow><mo>⇒</mo><msub><mi>S</mi><mrow><mi>A</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>O</mi></mrow></msub><mo>+</mo><msub><mi>S</mi><mrow><mi>C</mi><mo>⁢</mo><mi>D</mi><mo>⁢</mo><mi>O</mi></mrow></msub><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⁢</mo><msub><mi>S</mi><mrow><mi>A</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>C</mi><mo>⁢</mo><mi>D</mi></mrow></msub></mrow><mo mathvariant="italic"> </mo></mstyle></math> (1) (do <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><msub><mi>S</mi><mrow><mi>A</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>C</mi><mo>⁢</mo><mi>D</mi></mrow></msub><mo>=</mo><msub><mi>H</mi><mn>1</mn></msub><msub><mi>H</mi><mn>2</mn></msub><mo>.</mo><mi>A</mi><mi>B</mi><mo>)</mo></mstyle></math><br />Mà <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><msub><mi>S</mi><mrow><mi>B</mi><mo>⁢</mo><mi>C</mi><mo>⁢</mo><mi>O</mi></mrow></msub><mo>+</mo><msub><mi>S</mi><mrow><mi>D</mi><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mi>O</mi></mrow></msub><mo>+</mo><msub><mi>S</mi><mrow><mi>A</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>O</mi></mrow></msub><mo>+</mo><msub><mi>S</mi><mrow><mi>C</mi><mo>⁢</mo><mi>D</mi><mo>⁢</mo><mi>O</mi></mrow></msub><mo>=</mo><msub><mi>S</mi><mrow><mi>A</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>C</mi><mo>⁢</mo><mi>D</mi></mrow></msub></mstyle></math><br />Suy ra <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><msub><mi>S</mi><mrow><mi>B</mi><mo>⁢</mo><mi>C</mi><mo>⁢</mo><mi>O</mi></mrow></msub><mo>+</mo><msub><mi>S</mi><mrow><mi>D</mi><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mi>O</mi></mrow></msub><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⁢</mo><msub><mi>S</mi><mrow><mi>A</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>C</mi><mo>⁢</mo><mi>D</mi></mrow></msub></mstyle></math><br />Từ' (1) và (2) suy ra:<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⁢</mo><msub><mi>S</mi><mrow><mi>A</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>O</mi></mrow></msub><mo>+</mo><msub><mi>S</mi><mrow><mi>C</mi><mo>⁢</mo><mi>D</mi><mo>⁢</mo><mi>O</mi></mrow></msub><mo>=</mo><msub><mi>S</mi><mrow><mi>B</mi><mo>⁢</mo><mi>C</mi><mo>⁢</mo><mi>O</mi></mrow></msub><mo>+</mo><msub><mi>S</mi><mrow><mi>D</mi><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mi>O</mi></mrow></msub><mo>⁢</mo></math></p>
<p> </p>
Xem lời giải bài tập khác cùng bài
Hướng dẫn giải Bài 41 (Trang 132 SGK Toán Hình học 8, Tập 1)
Xem lời giải
Hướng dẫn giải Bài 42 (Trang 132 SGK Toán Hình học 8, Tập 1)
Xem lời giải
Hướng dẫn giải Bài 43 (Trang 133 SGK Toán Hình học 8, Tập 1)
Xem lời giải
Hướng dẫn giải Bài 45 (Trang 133 SGK Toán Hình học 8, Tập 1)
Xem lời giải
Hướng dẫn giải Bài 46 (Trang 133 SGK Toán Hình học 8, Tập 1)
Xem lời giải
Hướng dẫn giải Bài 47 (Trang 133 SGK Toán Hình học 8, Tập 1)
Xem lời giải