Ôn tập chương 2
Hướng dẫn giải Bài 43 (Trang 133 SGK Toán Hình học 8, Tập 1)
<p><strong class="content_question">Đề bài</strong></p>
<p>Cho hình vuông <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></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></math></span></span> có tâm đối xứng <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>O</mi></math>"><span id="MJXc-Node-7" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-8" class="mjx-mrow"><span id="MJXc-Node-9" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">O</span></span></span></span></span>, cạnh <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><mo>.</mo></math>"><span id="MJXc-Node-10" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-11" class="mjx-mrow"><span id="MJXc-Node-12" 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"><mo>.</mo></math></span></span> Một góc vuông <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>x</mi><mi>O</mi><mi>y</mi></math>"><span id="MJXc-Node-14" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-15" class="mjx-mrow"><span id="MJXc-Node-16" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">x</span></span><span id="MJXc-Node-17" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">Oy</span></span></span></span></span> có tia <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>O</mi><mi>x</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi><mi>x</mi></math></span></span> cắt cạnh <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>A</mi><mi>B</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>B</mi></math></span></span> tại <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>E</mi></math>"><span id="MJXc-Node-27" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-28" class="mjx-mrow"><span id="MJXc-Node-29" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span></span></span></span>, tia <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>O</mi><mi>y</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">O</span></span><span id="MJXc-Node-33" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">y</span></span></span></span></span> cắt cạnh <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>B</mi><mi>C</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">B</span></span></span></span><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math></span></span> tại <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>F</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math></span></span> (h.<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"><mn>161</mn></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>161</mn></math></span></span>)</p>
<p><img src="https://img.loigiaihay.com/picture/2018/0716/b43a-trang-133-sgk-toan-8-t-1-c2.jpg" /></p>
<p>Tính diện tích tứ giác <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>O</mi><mi>E</mi><mi>B</mi><mi>F</mi><mo>.</mo></math>"><span id="MJXc-Node-44" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-45" class="mjx-mrow"><span id="MJXc-Node-46" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">O</span></span><span id="MJXc-Node-47" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-48" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-49" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span><span id="MJXc-Node-50" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">.</span></span></span></span></span><br /><strong class="content_detail">Lời giải chi tiết</strong></p>
<p><img src="https://img.loigiaihay.com/picture/2018/0716/b43b-trang-133-sgk-toan-8-t-1-c2.jpg" /></p>
<p>Nối OA, OB.<br />Do ABCD là hình vuông nên O là trung điểm của AC, BD và <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mover accent="true"><mrow><mi>A</mi><mo>⁢</mo><mi>O</mi><mo>⁢</mo><mi>B</mi></mrow><mo>^</mo></mover><mo>=</mo><msup><mn>90</mn><mo>∘</mo></msup></mstyle></math><br />Ta có: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mover accent="true"><mrow><mi>A</mi><mo>⁢</mo><mi>O</mi><mo>⁢</mo><mi>E</mi></mrow><mo>^</mo></mover><mo>+</mo><mover accent="true"><mrow><mi>B</mi><mo>⁢</mo><mi>O</mi><mo>⁢</mo><mi>E</mi></mrow><mo>^</mo></mover><mo>=</mo><mover accent="true"><mrow><mi>A</mi><mo>⁢</mo><mi>O</mi><mo>⁢</mo><mi>B</mi></mrow><mo>^</mo></mover><mo>=</mo><msup><mn>90</mn><mn>0</mn></msup></mstyle></math><br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mover accent="true"><mrow><mi>F</mi><mo>⁢</mo><mi>O</mi><mo>⁢</mo><mi>B</mi></mrow><mo>^</mo></mover><mo>+</mo><mover accent="true"><mrow><mi>E</mi><mo>⁢</mo><mi>O</mi><mo>⁢</mo><mi>B</mi></mrow><mo>^</mo></mover><mo>=</mo><mover accent="true"><mrow><mi>x</mi><mo>⁢</mo><mi>O</mi><mo>⁢</mo><mi>y</mi></mrow><mo>^</mo></mover><mo>=</mo><msup><mn>90</mn><mn>0</mn></msup></mstyle></math><br />Nên <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mover accent="true"><mrow><mi>A</mi><mo>⁢</mo><mi>O</mi><mo>⁢</mo><mi>E</mi></mrow><mo>^</mo></mover><mo>=</mo><mover accent="true"><mrow><mi>B</mi><mo>⁢</mo><mi>O</mi><mo>⁢</mo><mi>F</mi></mrow><mo>^</mo></mover></mstyle></math> (cùng phụ với <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mover accent="true"><mrow><mi>B</mi><mo>⁢</mo><mi>O</mi><mo>⁢</mo><mi>E</mi></mrow><mo>^</mo></mover></mstyle></math>)<br />Xét <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi mathvariant="normal">△</mi><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mi>O</mi><mo>⁢</mo><mi>E</mi></mstyle></math> và <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi mathvariant="normal">△</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>O</mi><mo>⁢</mo><mi>F</mi></mstyle></math> có:<br />+) <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mover accent="true"><mrow><mi>A</mi><mo>⁢</mo><mi>O</mi><mo>⁢</mo><mi>E</mi></mrow><mo>^</mo></mover><mo>=</mo><mover accent="true"><mrow><mi>B</mi><mo>⁢</mo><mi>O</mi><mo>⁢</mo><mi>F</mi></mrow><mo>^</mo></mover></mstyle></math> (chứng minh trên)<br />+) OA=OB (O là tâm đối xứng của hình vuông)<br />+) <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mover accent="true"><mrow><mi>O</mi><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mi>E</mi></mrow><mo>^</mo></mover><mo>=</mo><mover accent="true"><mrow><mi>O</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>F</mi></mrow><mo>^</mo></mover><mo>=</mo><msup><mn>45</mn><mn>0</mn></msup></mstyle></math> (tính chất hình vuông)<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>⇒</mo><mi mathvariant="normal">Δ</mi><mi>A</mi><mi>O</mi><mi>E</mi><mo>=</mo><mi mathvariant="normal">Δ</mi><mi>B</mi><mi>O</mi><mi>F</mi><mo>(</mo><mi>g</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>g</mi><mo>)</mo></mstyle></math><br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>⇒</mo><msub><mi>S</mi><mrow><mi>A</mi><mo>⁢</mo><mi>O</mi><mo>⁢</mo><mi>E</mi></mrow></msub><mo>=</mo><msub><mi>S</mi><mrow><mi>B</mi><mo>⁢</mo><mi>O</mi><mo>⁢</mo><mi>F</mi></mrow></msub></mstyle></math><br />Do đó <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><msub><mi>S</mi><mrow><mi>O</mi><mo>⁢</mo><mi>E</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>F</mi></mrow></msub><mo>=</mo><msub><mi>S</mi><mrow><mi>O</mi><mo>⁢</mo><mi>E</mi><mo>⁢</mo><mi>B</mi></mrow></msub><mo>+</mo><msub><mi>S</mi><mrow><mi>O</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>F</mi></mrow></msub><mo>=</mo><msub><mi>S</mi><mrow><mi>O</mi><mo>⁢</mo><mi>E</mi><mo>⁢</mo><mi>B</mi></mrow></msub><mo>+</mo><msub><mi>S</mi><mrow><mi>O</mi><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mi>E</mi></mrow></msub><mo>=</mo><msub><mi>S</mi><mrow><mi>O</mi><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mi>B</mi></mrow></msub></mstyle></math><br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><msub><mi>S</mi><mrow><mi>O</mi><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mi>B</mi></mrow></msub><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⁢</mo><mi>O</mi><mo>⁢</mo><mi>A</mi><mo>⋅</mo><mi>O</mi><mo>⁢</mo><mi>B</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⋅</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mi>C</mi><mo>⋅</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⁢</mo><mi>B</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>4</mn></mfrac><mo>⋅</mo><mrow><mo>(</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>A</mi><mi>C</mi><mo>.</mo><mi>B</mi><mi>D</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><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 />Vậy <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><msub><mi>S</mi><mrow><mi>O</mi><mo>⁢</mo><mi>E</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>F</mi></mrow></msub><mo>=</mo><mfrac><mn>1</mn><mn>4</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><mo>=</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>⁢</mo><msup><mi>a</mi><mn>2</mn></msup></mstyle></math></p>
<p> </p>
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