Bài 7: Hình Bình Hành
Hướng dẫn giải Bài 45 (Trang 92 SGK Toán Hình học 8, Tập 1)
<p><strong class="content_question">Đề bài</strong></p>
<p>Cho hình bình hành <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 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> (<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><mo>&gt;</mo><mi>B</mi><mi>C</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">A</span></span><span id="MJXc-Node-10" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-11" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">></span></span><span id="MJXc-Node-12" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-13" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span></span></span></span>). Tia phân giác của góc <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>D</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">D</span></span></span></span></span> cắt <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></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">AB</span></span></span></span></span> ở <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>E</mi></math>"><span id="MJXc-Node-21" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-22" class="mjx-mrow"><span id="MJXc-Node-23" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span></span></span></span>, tia phân giác của góc B cắt <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>C</mi><mi>D</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mi>D</mi></math></span></span> ở <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>F</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">F</span></span></span></span></span>.</p>
<p>a) Chứng minh rằng <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>D</mi><mi>E</mi><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>B</mi><mi>F</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">D</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-texatom"><span id="MJXc-Node-39" class="mjx-mrow"><span id="MJXc-Node-40" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-41" class="mjx-texatom"><span id="MJXc-Node-42" class="mjx-mrow"><span id="MJXc-Node-43" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-44" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-45" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span></span></span></span>.</p>
<p>b) Tứ giác <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>D</mi><mi>E</mi><mi>B</mi><mi>F</mi></math>"><span id="MJXc-Node-46" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-47" class="mjx-mrow"><span id="MJXc-Node-48" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span><span id="MJXc-Node-49" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-50" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-51" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span></span></span></span> là hình gì ? Vì sao ?</p>
<p><strong>Lời giải chi tiết</strong> </p>
<p><img class="wscnph" style="max-width: 100%;" src="https://static.colearn.vn:8413/v1.0/upload/library/03072022/cc811a2d-59e7-421a-ac2e-91e5748fda27.PNG" /></p>
<p>a) Vì ABCD là hình bình hành (giả thiết)<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>⇒</mo><mover accent="true"><mrow><mi>A</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>C</mi></mrow><mo>^</mo></mover><mo>=</mo><mover accent="true"><mrow><mi>A</mi><mo>⁢</mo><mi>D</mi><mo>⁢</mo><mi>C</mi></mrow><mo>^</mo></mover></mstyle></math> (tính chất hình bình hành ) (1)<br />Vì BF là tia phân giác <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mover accent="true"><mrow><mi>A</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>C</mi></mrow><mo>^</mo></mover></mstyle></math> (giả thiết)<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>⇒</mo><mover accent="true"><msub><mi>B</mi><mn>1</mn></msub><mo>^</mo></mover><mo>=</mo><mover accent="true"><msub><mi>B</mi><mn>2</mn></msub><mo>^</mo></mover><mo>=</mo><mfrac><mover accent="true"><mrow><mi>A</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>C</mi></mrow><mo>^</mo></mover><mn>2</mn></mfrac></mstyle></math> (tính chất tia phân giác) (2)<br />Vì DE là tia phân giác <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mover accent="true"><mrow><mi>A</mi><mo>⁢</mo><mi>D</mi><mo>⁢</mo><mi>C</mi></mrow><mo>^</mo></mover></mstyle></math> (giả thiết)<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>⇒</mo><mover accent="true"><msub><mi>D</mi><mn>1</mn></msub><mo>^</mo></mover><mo>=</mo><mover accent="true"><msub><mi>D</mi><mn>2</mn></msub><mo>^</mo></mover><mo>=</mo><mfrac><mover accent="true"><mrow><mi>A</mi><mo>⁢</mo><mi>D</mi><mo>⁢</mo><mi>C</mi></mrow><mo>^</mo></mover><mn>2</mn></mfrac></mstyle></math> (tính chất tia phân giác) (3)<br />Từ' <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>1</mn><mo>)</mo><mo>,</mo><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow><mo>⇒</mo><mover accent="true"><msub><mi>D</mi><mn>2</mn></msub><mo>^</mo></mover><mo>=</mo><mover accent="true"><msub><mi>B</mi><mn>1</mn></msub><mo>^</mo></mover></math> (4)<br />Có AB//DC (vì ABCD là hình bình hành)<br />Suy ra: <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mover accent="true"><msub><mi>B</mi><mn>1</mn></msub><mo>^</mo></mover><mo>=</mo><mover accent="true"><msub><mi>F</mi><mn>1</mn></msub><mo>^</mo></mover></mstyle></math> (so le trong) (5)<br />Từ' (4) và (5) suy ra <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mover accent="true"><msub><mi>F</mi><mn>1</mn></msub><mo>^</mo></mover><mo>=</mo><mover accent="true"><msub><mi>D</mi><mn>2</mn></msub><mo>^</mo></mover></mstyle></math> mà hai góc này ở vị trí đồng vị nên DE//BF (dấu hiệu nhận biết hai đường thẳng song song)<br />b) ABCD là hình bình hành (giả thiết)<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>⇒</mo><mi>A</mi><mi>B</mi><mo>/</mo><mo>/</mo><mi>C</mi><mi>D</mi></mstyle></math> (tính chất hình bình hành) hay BE//DF<br />Xét tứ giác DEBF có BE//DF (chứng minh trên) và DE//BF (theo câu a)<br />Suy ra tứ giác DEBF là hình bình hành (dấu hiệu nhận biết hình bình hành).</p>
<p> </p>
Xem lời giải bài tập khác cùng bài
Hướng dẫn giải Bài 43 (Trang 92 SGK Toán Hình học 8, Tập 1)
Xem lời giải
Hướng dẫn giải Bài 44 (Trang 92 SGK Toán Hình học 8, Tập 1)
Xem lời giải
Hướng dẫn giải Bài 46 (Trang 92 SGK Toán Hình học 8, Tập 1)
Xem lời giải
Hướng dẫn giải Bài 47 (Trang 93 SGK Toán Hình học 8, Tập 1)
Xem lời giải
Hướng dẫn giải Bài 48 (Trang 93 SGK Toán Hình học 8, Tập 1)
Xem lời giải
Hướng dẫn giải Bài 49 (Trang 93 SGK Toán Hình học 8, Tập 1)
Xem lời giải