Bài 7: Hình Bình Hành
Hướng dẫn giải Bài 47 (Trang 93 SGK Toán Hình học 8, Tập 1)
<p>Cho hình <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: 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"><mn>72</mn></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-mn"><span class="mjx-char MJXc-TeX-main-R">72</span></span></span></span></span>, trong đó <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: 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>A</mi><mi>B</mi><mi>C</mi><mi>D</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">A</span></span><span id="MJXc-Node-7" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-8" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-9" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span></span></span></span> là hình bình hành.<br /><br /><img class="wscnph" style="max-width: 100%;" src="https://static.colearn.vn:8413/v1.0/upload/library/03072022/28287939-ca91-4abc-9c75-ea07b1928222.PNG" /></p>
<p>LG a.<br />Chứng minh rằng AHCK là hình bình hành.<br />Phương pháp giải:<br />Áp dụng: Dấu hiệu nhận biết hình bình hành: Tứ giác có hai cạnh đô song và bằng nhau là hình bình hành.<br />Lời giải chi tiết:<br />Xét hai tam giác vuông AHD và CKB có:<br />+) AD=CB (vì ABCD là hình bình hành)<br />+) <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>H</mi></mrow><mo>^</mo></mover><mo>=</mo><mover accent="true"><mrow><mi>C</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>K</mi></mrow><mo>^</mo></mover></mstyle></math> (hai góc ở vị trí so le trong, AD//BC)<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>⇒</mo><mi mathvariant="normal">Δ</mi><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mi>H</mi><mo>⁢</mo><mi>D</mi><mo>=</mo><mi mathvariant="normal">Δ</mi><mo>⁢</mo><mi>C</mi><mo>⁢</mo><mi>K</mi><mo>⁢</mo><mi>B</mi></mstyle></math> (cạnh huyền- góc nhọn)<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>⇒</mo><mi>A</mi><mo>⁢</mo><mi>H</mi><mo>=</mo><mi>C</mi><mo>⁢</mo><mi>K</mi></mstyle></math> ( 2 cạnh tương ứng)<br />Ta có:<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>A</mi><mo>⁢</mo><mi>H</mi><mo>⟂</mo><mi>B</mi><mo>⁢</mo><mpadded><mi mathvariant="normal">D</mi></mpadded></mtd></mtr><mtr><mtd><mi>C</mi><mo>⁢</mo><mi>K</mi><mo>⟂</mo><mi>B</mi><mo>⁢</mo><mi mathvariant="normal">D</mi></mtd></mtr></mtable></mfenced></mstyle></math> (giả thiết) <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>⇒</mo><mi>A</mi><mi>H</mi><mo>/</mo><mo>/</mo><mi>C</mi><mi>K</mi></mstyle></math><br />Xét tứ giác AHCK có:<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>A</mi><mi>H</mi><mo>/</mo><mo>/</mo><mi>C</mi><mpadded><mi>K</mi></mpadded></mtd></mtr><mtr><mtd><mi>A</mi><mi>H</mi><mo>=</mo><mi>C</mi><mi>K</mi></mtd></mtr></mtable></mfenced></mstyle></math>(chứng minh trên)<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>⇒</mo></mstyle></math> tứ giác AHCK là hình bình hành (dấu hiệu nhận biết hình bình hành)</p>
<p><strong>Câu 2</strong></p>
<p>Gọi <span id="MathJax-Element-20-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-188" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-189" class="mjx-mrow"><span id="MJXc-Node-190" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">O</span></span></span></span></span> là trung điểm của <span id="MathJax-Element-21-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>H</mi><mi>K</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mi>K</mi></math></span></span>. Chứng minh rằng ba điểm <span id="MathJax-Element-22-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><mi>O</mi><mo>,</mo><mi>C</mi></math>"><span id="MJXc-Node-195" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-196" class="mjx-mrow"><span id="MJXc-Node-197" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-198" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-199" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">O</span></span><span id="MJXc-Node-200" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-201" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">C</span></span></span></span></span> thẳng hàng</p>
<p><strong>Phương pháp giải:</strong></p>
<p>Áp dụng: Tính chất hình bình hành: Hai đường chéo cắt nhau tại trung điểm của mỗi đường.</p>
<p><strong>Lời giải chi tiết:</strong></p>
<p>Xét hình bình hành <span id="MathJax-Element-23-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>H</mi><mi>C</mi><mi>K</mi></math>"><span id="MJXc-Node-202" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-203" class="mjx-mrow"><span id="MJXc-Node-204" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-205" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">H</span></span><span id="MJXc-Node-206" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-207" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">K</span></span></span></span></span> có <span id="MathJax-Element-24-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 class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi></math></span></span> là trung điểm của <span id="MathJax-Element-25-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>H</mi><mi>K</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mi>K</mi></math></span></span> (giả thiết)</p>
<p><span id="MathJax-Element-26-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"><mo stretchy="false">&#x21D2;</mo></math>"><span id="MJXc-Node-215" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-216" class="mjx-mrow"><span id="MJXc-Node-217" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">⇒</span></span></span></span></span> <span id="MathJax-Element-27-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-218" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-219" class="mjx-mrow"><span id="MJXc-Node-220" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">O</span></span></span></span></span> là giao điểm của hai đường chéo <span id="MathJax-Element-28-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>C</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>C</mi></math></span></span> và <span id="MathJax-Element-29-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>H</mi><mi>K</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mi>K</mi></math></span></span> của hình bình hành (tính chất hình bình hành)</p>
<p>Hay <span id="MathJax-Element-30-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><mi>O</mi><mo>,</mo><mi>C</mi></math>"><span id="MJXc-Node-229" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-230" class="mjx-mrow"><span id="MJXc-Node-231" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-232" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-233" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">O</span></span><span id="MJXc-Node-234" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-235" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">C</span></span></span></span></span> thẳng hàng.</p>
<p> </p>
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