Bài 2: Hình Thang
Hướng dẫn giải Bài 8 (Trang 71 SGK Toán Hình học 8, Tập 1)
<p><strong class="content_question">Đề bài</strong></p>
<p>Hình thang ABCD (AB//CD) có <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mover accent="true"><mi>A</mi><mo>^</mo></mover><mo>-</mo><mover accent="true"><mi>D</mi><mo>^</mo></mover><mo>=</mo><msup><mn>20</mn><mo>∘</mo></msup><mo>,</mo><mover accent="true"><mi>B</mi><mo>^</mo></mover><mo>=</mo><mn>2</mn><mo>⁢</mo><mover accent="true"><mi>C</mi><mo>^</mo></mover></mstyle></math>. Tính các góc của hình thang.</p>
<p><strong class="content_detail">Lời giải chi tiết</strong></p>
<p><img src="https://vietjack.com/giai-toan-lop-8/images/bai-8-trang-71-sgk-toan-8-tap-1-7.PNG" alt="Giải bài 8 trang 71 Toán 8 Tập 1 | Giải bài tập Toán 8" /></p>
<p><span class="content_detail">Vì AB//CD nên <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mover accent="true"><mi>A</mi><mo>^</mo></mover><mo>+</mo><mover accent="true"><mi>D</mi><mo>^</mo></mover><mo>=</mo><msup><mn>180</mn><mn>0</mn></msup></mstyle></math> (1) (hai góc trong cùng phía bù nhau)<br />Ta có <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mover accent="true"><mi>A</mi><mo>^</mo></mover><mo>-</mo><mover accent="true"><mi>D</mi><mo>^</mo></mover><mo>=</mo><msup><mn>20</mn><mn>0</mn></msup></mstyle></math> (giả thiết) <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>⇒</mo><mover accent="true"><mi>A</mi><mo>^</mo></mover><mo>=</mo><mover accent="true"><mi>D</mi><mo>^</mo></mover><mo>+</mo><msup><mn>20</mn><mn>0</mn></msup></mstyle></math> (2)<br />Thay (2) vào (1) ta được:<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>⇒</mo><mover accent="true"><mi>A</mi><mo>^</mo></mover><mo>+</mo><mover accent="true"><mi>D</mi><mo>^</mo></mover><mo>=</mo><mover accent="true"><mi>D</mi><mo>^</mo></mover><mo>+</mo><msup><mn>20</mn><mn>0</mn></msup><mo>+</mo><mpadded><mover accent="true"><mi>D</mi><mo>^</mo></mover></mpadded><mo>=</mo><mn>2</mn><mo>⁢</mo><mover accent="true"><mi>D</mi><mo>^</mo></mover><mo>+</mo><msup><mn>20</mn><mn>0</mn></msup><mo>=</mo><mpadded><msup><mn>180</mn><mn>0</mn></msup></mpadded></mrow><mspace linebreak="newline"/><mrow><mo>⇒</mo><mover accent="true"><mi>D</mi><mo>^</mo></mover><mo>=</mo><mrow><mo>(</mo><msup><mn>180</mn><mn>0</mn></msup><mo>-</mo><msup><mn>20</mn><mn>0</mn></msup><mo>)</mo></mrow></mrow><mo>:</mo><mn>2</mn><mo>=</mo><msup><mn>80</mn><mn>0</mn></msup><mo>.</mo></math><br />Thay <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mover accent="true"><mi>D</mi><mo>^</mo></mover><mo>=</mo><msup><mn>80</mn><mn>0</mn></msup></mstyle></math> ta được <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mover accent="true"><mi>A</mi><mo>^</mo></mover><mo>=</mo><msup><mn>20</mn><mn>0</mn></msup><mo>+</mo><msup><mn>80</mn><mn>0</mn></msup><mo>=</mo><msup><mn>100</mn><mn>0</mn></msup></mstyle></math><br />Lại có <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mover accent="true"><mi>B</mi><mo>^</mo></mover><mo>=</mo><mn>2</mn><mo>⁢</mo><mover accent="true"><mi>C</mi><mo>^</mo></mover></mstyle></math> (3);<br />Do AB//CD nên <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mover accent="true"><mi>B</mi><mo>^</mo></mover><mo>+</mo><mover accent="true"><mi>C</mi><mo>^</mo></mover><mo>=</mo><msup><mn>180</mn><mo>∘</mo></msup></mstyle></math> (4) (hai góc trong cùng phía bù nhau)<br />Thay (3) vào (4) ta được:<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mover accent="true"><mi>C</mi><mo>^</mo></mover><mo>+</mo><mover accent="true"><mi>C</mi><mo>^</mo></mover><mo>=</mo><msup><mn>180</mn><mn>0</mn></msup></math><br />hay <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mover accent="true"><mi>C</mi><mo>^</mo></mover><mo>=</mo><msup><mn>180</mn><mo>∘</mo></msup><mo>⇒</mo><mover accent="true"><mi>C</mi><mo>^</mo></mover><mo>=</mo><msup><mn>180</mn><mo>∘</mo></msup></mrow><mo>:</mo><mn>3</mn><mo>=</mo><msup><mn>60</mn><mo>∘</mo></msup></math><br /></span><span class="content_detail">Do đó <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mover accent="true"><mi>B</mi><mo>^</mo></mover><mo>=</mo><mn>2</mn><mo>⁢</mo><mover accent="true"><mi>C</mi><mo>^</mo></mover><mo>=</mo><msup><mn>2.60</mn><mn>0</mn></msup><mo>=</mo><msup><mn>120</mn><mn>0</mn></msup></mstyle></math></span><strong class="content_detail"><br /></strong></p>
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