Bài 2: Hình Thang
Hướng dẫn giải Bài 7 (Trang 71 SGK Toán Hình học 8, Tập 1)
<p><strong class="content_question">Đề bài</strong></p>
<p>Tìm <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>x</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">x</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>y</mi></math>"><span id="MJXc-Node-4" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-5" class="mjx-mrow"><span id="MJXc-Node-6" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">y</span></span></span></span></span> trên hình <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"><mn>21</mn></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-mn"><span class="mjx-char MJXc-TeX-main-R">21</span></span></span></span></span>, biết rằng <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>A</mi><mi>B</mi><mi>C</mi><mi>D</mi></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 id="MJXc-Node-13" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-14" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-15" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span></span></span></span> là hình thang có đáy là <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>A</mi><mi>B</mi></math>"><span id="MJXc-Node-16" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-17" class="mjx-mrow"><span id="MJXc-Node-18" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-19" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span></span></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>C</mi><mi>D</mi><mo>.</mo></math>"><span id="MJXc-Node-20" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-21" class="mjx-mrow"><span id="MJXc-Node-22" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-23" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span><span id="MJXc-Node-24" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">.</span></span></span></span></span></p>
<p><img src="https://vietjack.com/giai-toan-lop-8/images/bai-7-trang-71-sgk-toan-8-tap-1.PNG" alt="Giải bài 7 trang 71 Toán 8 Tập 1 | Giải bài tập Toán 8" /></p>
<p><strong class="content_detail">Lời giải chi tiết</strong></p>
<p>Vì <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>A</mi><mi>B</mi><mi>C</mi><mi>D</mi></math>"><span id="MJXc-Node-25" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-26" class="mjx-mrow"><span id="MJXc-Node-27" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-28" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-29" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-30" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span></span></span></span> là hình thang có đáy là <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>A</mi><mi>B</mi></math>"><span id="MJXc-Node-31" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-32" class="mjx-mrow"><span id="MJXc-Node-33" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-34" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span></span></span></span> và <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>C</mi><mi>D</mi></math>"><span id="MJXc-Node-35" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-36" class="mjx-mrow"><span id="MJXc-Node-37" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-38" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span></span></span></span> nên <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>A</mi><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>C</mi><mi>D</mi></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">A</span></span><span id="MJXc-Node-42" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-43" class="mjx-texatom"><span id="MJXc-Node-44" class="mjx-mrow"><span id="MJXc-Node-45" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-46" class="mjx-texatom"><span id="MJXc-Node-47" class="mjx-mrow"><span id="MJXc-Node-48" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-49" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-50" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span></span></span></span></p>
<p><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"><mi>a</mi><mo stretchy="false">)</mo></math>"><span id="MJXc-Node-51" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-52" class="mjx-mrow"><span id="MJXc-Node-53" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">a</span></span><span id="MJXc-Node-54" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">)</span></span></span></span></span> Ta có: <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: 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><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>D</mi><mi>C</mi></math>"><span id="MJXc-Node-55" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-56" class="mjx-mrow"><span id="MJXc-Node-57" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-58" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-59" class="mjx-texatom"><span id="MJXc-Node-60" class="mjx-mrow"><span id="MJXc-Node-61" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-62" class="mjx-texatom"><span id="MJXc-Node-63" class="mjx-mrow"><span id="MJXc-Node-64" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-65" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">DC</span></span></span></span></span> (chứng minh trên) </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><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>180</mn><mn>0</mn></msup><mo> </mo><mo>(</mo><mi>h</mi><mi>a</mi><mi>i</mi><mo> </mo><mi>g</mi><mi>ó</mi><mi>c</mi><mo> </mo><mi>t</mi><mi>r</mi><mi>o</mi><mi>n</mi><mi>g</mi><mo> </mo><mi>c</mi><mi>ù</mi><mi>n</mi><mi>g</mi><mo> </mo><mi>p</mi><mi>h</mi><mi>í</mi><mi>a</mi><mo> </mo><mi>b</mi><mi>ù</mi><mo> </mo><mi>n</mi><mi>h</mi><mi>a</mi><mi>u</mi><mo>)</mo><mspace linebreak="newline"></mspace><mo>⇒</mo><mi>x</mi><mo>+</mo><msup><mn>80</mn><mn>0</mn></msup><mo>=</mo><mpadded><msup><mn>180</mn><mo>∘</mo></msup></mpadded><mo></mo><mspace linebreak="newline"></mspace><mo>⇒</mo><mi>x</mi><mo>=</mo><msup><mn>180</mn><mn>0</mn></msup><mo>-</mo><msup><mn>80</mn><mn>0</mn></msup><mo>=</mo><msup><mn>100</mn><mo>∘</mo></msup><mo></mo></math></p>
<p>Ta có: AB //DC (chứng minh trên)<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mover accent="true"><mi>C</mi><mo>^</mo></mover><mo>+</mo><mover accent="true"><mi>B</mi><mo>^</mo></mover><mo>=</mo><msup><mn>180</mn><mo>∘</mo></msup><mo> </mo><mo>(</mo><mi>h</mi><mi>a</mi><mi>i</mi><mo> </mo><mi>g</mi><mi>ó</mi><mi>c</mi><mo> </mo><mi>đ</mi><mi>ồ</mi><mi>n</mi><mi>g</mi><mo> </mo><mi>v</mi><mi>ị</mi><mo> </mo><mi>b</mi><mi>ằ</mi><mi>n</mi><mi>g</mi><mo> </mo><mi>n</mi><mi>h</mi><mi>a</mi><mi>u</mi><mo>)</mo><mspace linebreak="newline"></mspace><mo>⇒</mo><mi>y</mi><mo>+</mo><msup><mn>40</mn><mn>0</mn></msup><mo>=</mo><mpadded><msup><mn>180</mn><mo>∘</mo></msup></mpadded><mspace linebreak="newline"></mspace><mo>⇒</mo><mi>y</mi><mo>=</mo><msup><mn>180</mn><mn>0</mn></msup><mo>-</mo><msup><mn>40</mn><mo>∘</mo></msup><mo>=</mo><msup><mn>140</mn><mo>∘</mo></msup></math><br />b) Vì AB//DC (chứng minh trên)<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>⇒</mo><mi>x</mi><mo>=</mo><msup><mn>70</mn><mn>0</mn></msup></mstyle></math> (hai góc đồng vị bằng nhau)<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>⇒</mo><mi>y</mi><mo>=</mo><msup><mn>50</mn><mn>0</mn></msup></mstyle></math> (hai góc so le trong bằng nhau)<br />c) Ta có AB//DC (chứng minh trên)<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>⇒</mo><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><mn>0</mn></msup></mstyle></math> (hai góc trong cùng phía bù nhau)<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><msup><mn>90</mn><mn>0</mn></msup><mo>=</mo><mpadded><msup><mn>180</mn><mn>0</mn></msup></mpadded><mspace linebreak="newline"></mspace><mo>⇒</mo><mi>x</mi><mo>=</mo><msup><mn>180</mn><mn>0</mn></msup><mo>-</mo><msup><mn>90</mn><mn>0</mn></msup><mo>=</mo><msup><mn>90</mn><mn>0</mn></msup></math><br />Ta có AB//DC (chứng minh trên)</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mover accent="true"><mi>D</mi><mo>^</mo></mover><mo>+</mo><mover accent="true"><mi>A</mi><mo>^</mo></mover><mo>=</mo><msup><mn>180</mn><mn>0</mn></msup><mo> </mo><mo>(</mo><mi>h</mi><mi>a</mi><mi>i</mi><mo> </mo><mi>g</mi><mi>ó</mi><mi>c</mi><mo> </mo><mi>t</mi><mi>r</mi><mi>o</mi><mi>n</mi><mi>g</mi><mo> </mo><mi>c</mi><mi>ù</mi><mi>n</mi><mi>g</mi><mo> </mo><mi>p</mi><mi>h</mi><mi>í</mi><mi>a</mi><mo> </mo><mi>b</mi><mi>ù</mi><mo> </mo><mi>n</mi><mi>h</mi><mi>a</mi><mi>u</mi><mo>)</mo><mspace linebreak="newline"></mspace><mo>⇒</mo><mi>y</mi><mo>+</mo><msup><mn>65</mn><mn>0</mn></msup><mo>=</mo><mpadded><msup><mn>180</mn><mn>0</mn></msup></mpadded><mspace linebreak="newline"></mspace><mo>⇒</mo><mi>y</mi><mo>=</mo><msup><mn>180</mn><mn>0</mn></msup><mo>-</mo><msup><mn>65</mn><mn>0</mn></msup><mo>=</mo><msup><mn>115</mn><mn>0</mn></msup></math></p>
<p> </p>
<p> </p>
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