Bài 11: Hình Thoi
Hướng dẫn giải Bài 75 (Trang 106 SGK Toán Hình học 8, Tập 1)
<p><strong class="content_question">Đề bài</strong></p>
<p>Chứng minh rằng các trung điểm của bốn cạnh của một hình chữ nhật là các đỉnh của hình thoi.</p>
<p><strong class="content_detail">Lời giải chi tiết</strong></p>
<p><img class="wscnph" style="max-width: 100%;" src="https://static.colearn.vn:8413/v1.0/upload/library/06072022/b75-trand-106-sdk-toan-8-t-1-c2-6hyrBI.jpg" /></p>
<p>Giả sử hình chữ nhật ABCD có E, F, G, H lần lượt là trung điểm của AB, BC, CD, DA<br />Bốn tam giác vuông EAH, EBF, GDH, GCF có:<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>E</mi><mo>=</mo><mi>B</mi><mi>E</mi><mo>=</mo><mi>D</mi><mi>G</mi><mo>=</mo><mi>C</mi><mi>G</mi><mrow><mo>(</mo><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>A</mi><mi>B</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>C</mi><mi>D</mi><mo>)</mo></mrow><mspace linebreak="newline"/><mi>H</mi><mi>A</mi><mo>=</mo><mi>F</mi><mi>B</mi><mo>=</mo><mi>D</mi><mi>H</mi><mo>=</mo><mi>C</mi><mi>F</mi><mrow><mo>(</mo><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>A</mi><mi>D</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>B</mi><mi>C</mi><mo>)</mo></mrow></math><br />Xét <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi mathvariant="normal">Δ</mi><mo>⁢</mo><mi>E</mi><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mi>H</mi></mstyle></math> và <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi mathvariant="normal">Δ</mi><mo>⁢</mo><mi>E</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>F</mi></mstyle></math> có:<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>A</mi><mo>⁢</mo><mi mathvariant="normal">E</mi><mo>=</mo><mi>B</mi><mo>⁢</mo><mi>E</mi><mo>⁢</mo><mrow><mo>(</mo><mi>c</mi><mo>⁢</mo><mi>m</mi><mo>⁢</mo><mi>t</mi><mo>)</mo></mrow></mtd></mtr><mtr><mtd><mover accent="true"><mi>A</mi><mo>^</mo></mover><mo>=</mo><mover accent="true"><mi>B</mi><mo>^</mo></mover><mo>=</mo><msup><mn>90</mn><mn>0</mn></msup><mo>(</mo><mi>g</mi><mo>⁢</mo><mi>t</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mo>⁢</mo><mi>H</mi><mo>=</mo><mi>B</mi><mo>⁢</mo><mi>F</mi><mo>⁢</mo><mrow><mo>(</mo><mi>c</mi><mo>⁢</mo><mi>m</mi><mo>⁢</mo><mi>t</mi><mo>)</mo></mrow></mtd></mtr></mtable></mfenced><mo>⁢</mo><mspace linebreak="newline"/><mo>⇒</mo><mi mathvariant="normal">Δ</mi><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mi>H</mi><mo>⁢</mo><mi>E</mi><mo>=</mo><mi mathvariant="normal">Δ</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>E</mi><mo>⁢</mo><mi>F</mi><mo>⁢</mo><mrow><mo>(</mo><mi>c</mi><mo>-</mo><mi>g</mi><mo>-</mo><mi>c</mi><mo>)</mo></mrow><mo>⁢</mo><mspace linebreak="newline"/><mo>⇒</mo><mi>E</mi><mo>⁢</mo><mi>H</mi><mo>=</mo><mi>E</mi><mo>⁢</mo><mi>F</mi><mo>⁢</mo><mrow><mo>(</mo><mn>2</mn><mo>⁢</mo><mi>c</mi><mi>ạ</mi><mi>n</mi><mi>h</mi><mo> </mo><mi>t</mi><mi>ư</mi><mi>ơ</mi><mi>n</mi><mi>g</mi><mo> </mo><mi>ứ</mi><mi>n</mi><mi>g</mi><mo>)</mo></mrow><mo>⁢</mo><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mo>⁢</mo></math><br />Xét <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi mathvariant="normal">Δ</mi><mo>⁢</mo><mi>H</mi><mo>⁢</mo><mi>D</mi><mo>⁢</mo><mi>G</mi></mstyle></math> và <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi mathvariant="normal">Δ</mi><mo>⁢</mo><mi>F</mi><mo>⁢</mo><mi>C</mi><mo>⁢</mo><mi>G</mi></mstyle></math> có:<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>H</mi><mo>⁢</mo><mi mathvariant="normal">D</mi><mo>=</mo><mi>F</mi><mo>⁢</mo><mi>C</mi><mo>⁢</mo><mrow><mo>(</mo><mi>c</mi><mo>⁢</mo><mi>m</mi><mo>⁢</mo><mi>t</mi><mo>)</mo></mrow></mtd></mtr><mtr><mtd><mover accent="true"><mi>D</mi><mo>^</mo></mover><mo>=</mo><mover accent="true"><mi>C</mi><mo>^</mo></mover><mo>=</mo><msup><mn>90</mn><mn>0</mn></msup><mo>(</mo><mi>g</mi><mo>⁢</mo><mi>t</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>D</mi><mo>⁢</mo><mi>G</mi><mo>=</mo><mi>C</mi><mo>⁢</mo><mi>G</mi><mo>⁢</mo><mrow><mo>(</mo><mi>c</mi><mo>⁢</mo><mi>m</mi><mo>⁢</mo><mi>t</mi><mo>)</mo></mrow></mtd></mtr></mtable></mfenced><mo>⁢</mo><mspace linebreak="newline"/><mo>⇒</mo><mi mathvariant="normal">Δ</mi><mo>⁢</mo><mi>H</mi><mo>⁢</mo><mi>D</mi><mo>⁢</mo><mi>G</mi><mo>=</mo><mi mathvariant="normal">Δ</mi><mo>⁢</mo><mi>F</mi><mo>⁢</mo><mi>C</mi><mo>⁢</mo><mi>G</mi><mo>⁢</mo><mrow><mo>(</mo><mi>c</mi><mo>-</mo><mi>g</mi><mo>-</mo><mi>c</mi><mo>)</mo></mrow><mo>⁢</mo><mspace linebreak="newline"/><mo>⇒</mo><mi>G</mi><mo>⁢</mo><mi>H</mi><mo>=</mo><mi>G</mi><mo>⁢</mo><mi>F</mi><mo>⁢</mo><mo>⁢</mo><mrow><mo>(</mo><mn>2</mn><mo>⁢</mo><mi>c</mi><mi>ạ</mi><mi>n</mi><mi>h</mi><mo> </mo><mi>t</mi><mi>ư</mi><mi>ơ</mi><mi>n</mi><mi>g</mi><mo> </mo><mi>ứ</mi><mi>n</mi><mi>g</mi><mo>)</mo></mrow><mo>⁢</mo><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></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>H</mi><mo>⁢</mo><mi>E</mi></mstyle></math> và <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi mathvariant="normal">Δ</mi><mo>⁢</mo><mi>D</mi><mo>⁢</mo><mi>H</mi><mo>⁢</mo><mi>G</mi></mstyle></math> có:<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mpadded><mi>H</mi></mpadded><mo>⁢</mo><mi mathvariant="normal">A</mi><mo>=</mo><mi>H</mi><mo>⁢</mo><mi>D</mi><mo>⁢</mo><mrow><mo>(</mo><mi>c</mi><mo>⁢</mo><mi>m</mi><mo>⁢</mo><mi>t</mi><mo>)</mo></mrow></mtd></mtr><mtr><mtd><mover accent="true"><mi>A</mi><mo>^</mo></mover><mo>=</mo><mover accent="true"><mi>D</mi><mo>^</mo></mover><mo>=</mo><msup><mn>90</mn><mn>0</mn></msup><mo>⁢</mo><mrow><mo>(</mo><mi>g</mi><mo>⁢</mo><mi>t</mi><mo>)</mo></mrow></mtd></mtr><mtr><mtd><mi>A</mi><mo>⁢</mo><mi>E</mi><mo>=</mo><mi>D</mi><mo>⁢</mo><mi>G</mi><mo>⁢</mo><mrow><mo>(</mo><mi>c</mi><mo>⁢</mo><mi>m</mi><mo>⁢</mo><mi>t</mi><mo>)</mo></mrow></mtd></mtr></mtable></mfenced></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi mathvariant="normal">Δ</mi><mi>A</mi><mi>H</mi><mi>E</mi><mo>=</mo><mi mathvariant="normal">Δ</mi><mi>D</mi><mi>H</mi><mi>G</mi><mrow><mo>(</mo><mi>c</mi><mo>-</mo><mi>g</mi><mo>-</mo><mi>c</mi><mo>)</mo></mrow><mspace linebreak="newline"/><mo>⇒</mo><mi>E</mi><mi>H</mi><mo>=</mo><mi>H</mi><mi>G</mi><mrow><mo>(</mo><mn>2</mn><mo> </mo><mo> </mo><mi>c</mi><mi>ạ</mi><mi>n</mi><mi>h</mi><mo> </mo><mi>t</mi><mi>ư</mi><mi>ơ</mi><mi>n</mi><mi>g</mi><mo> </mo><mi>ứ</mi><mi>n</mi><mi>g</mi><mo>)</mo><mo> </mo><mo> </mo></mrow><mspace linebreak="newline"/><mi>T</mi><mi>ừ</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow><mo> </mo><mo> </mo><mi>v</mi><mi>à</mi><mi mathvariant="normal"> </mi><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow><mo>⇒</mo><mi>H</mi><mi>E</mi><mo>=</mo><mi>E</mi><mi>F</mi><mo>=</mo><mi>H</mi><mi>G</mi><mo>=</mo><mi>G</mi><mi>F</mi><mspace linebreak="newline"/></math></p>
<p><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"><mo stretchy="false">&#x21D2;</mo></math>"><span id="MJXc-Node-460" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-461" class="mjx-mrow"><span id="MJXc-Node-462" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">⇒</span></span></span></span></span><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>E</mi><mi>F</mi><mi>G</mi><mi>H</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>F</mi><mi>G</mi><mi>H</mi></math></span></span> là hình thoi (dấu hiệu nhận biết hình thoi).</p>
<p>(Trong đó: "cmt" là chứng minh trên) </p>
<p><strong>Cách khác:</strong></p>
<p>* Xét tam giác <span id="MathJax-Element-31-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>D</mi></math>"><span id="MJXc-Node-469" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-470" class="mjx-mrow"><span id="MJXc-Node-471" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-472" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-473" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span></span></span></span> có <span id="MathJax-Element-32-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-474" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-475" class="mjx-mrow"><span id="MJXc-Node-476" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span></span></span></span> và <span id="MathJax-Element-33-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></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi></math></span></span> lần lượt là trung điểm của <span id="MathJax-Element-34-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-480" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-481" class="mjx-mrow"><span id="MJXc-Node-482" 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"><mi>B</mi></math></span></span> và <span id="MathJax-Element-35-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>D</mi></math>"><span id="MJXc-Node-484" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-485" class="mjx-mrow"><span id="MJXc-Node-486" 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"><mi>D</mi></math></span></span></p>
<p>Suy ra <span id="MathJax-Element-36-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><mi>H</mi></math>"><span id="MJXc-Node-488" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-489" class="mjx-mrow"><span id="MJXc-Node-490" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span></span></span><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi></math></span></span> là đường trung bình của tam giác</p>
<p>Từ đó <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo>=</mo><mfrac><mrow><mi>B</mi><mo>⁢</mo><mi>D</mi></mrow><mn>2</mn></mfrac><mrow><mo>(</mo><mmultiscripts><mo>)</mo><mprescripts/><none/><mo>*</mo></mmultiscripts></mrow></math><br />Chứng minh tương tự ta có: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mi>F</mi><mo>=</mo><mfrac><mrow><mi>B</mi><mo>⁢</mo><mi>D</mi></mrow><mn>2</mn></mfrac><mo>,</mo><mi>E</mi><mo>⁢</mo><mi>F</mi><mo>=</mo><mfrac><mrow><mi>A</mi><mo>⁢</mo><mi>C</mi></mrow><mn>2</mn></mfrac><mo>,</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi>H</mi><mi>G</mi><mo>=</mo><mfrac><mrow><mi>A</mi><mo>⁢</mo><mi>C</mi></mrow><mn>2</mn></mfrac><mo>(</mo><mmultiscripts><mo>)</mo><mprescripts/><none/><mrow><mo>*</mo><mo>*</mo></mrow></mmultiscripts></mstyle></math></p>
<p>Vì <span id="MathJax-Element-41-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-540" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-541" class="mjx-mrow"><span id="MJXc-Node-542" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-543" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-544" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-545" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span></span></span></span> là hình chữ nhật nên <span id="MathJax-Element-42-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><mo>=</mo><mi>B</mi><mi>D</mi></math>"><span id="MJXc-Node-546" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-547" class="mjx-mrow"><span id="MJXc-Node-548" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-549" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-550" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-551" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-552" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span></span></span></span> (***) (tính chất)</p>
<p>Từ (*), (**), (***) ta suy ra <span id="MathJax-Element-43-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><mi>H</mi><mo>=</mo><mi>E</mi><mi>F</mi><mo>=</mo><mi>H</mi><mi>G</mi><mo>=</mo><mi>G</mi><mi>F</mi></math>"><span id="MJXc-Node-553" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-554" class="mjx-mrow"><span id="MJXc-Node-555" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-556" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">H</span></span><span id="MJXc-Node-557" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-558" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-559" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span><span id="MJXc-Node-560" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-561" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">H</span></span><span id="MJXc-Node-562" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">G=GF</span></span></span></span></span></p>
<p><span id="MathJax-Element-44-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-566" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-567" class="mjx-mrow"><span id="MJXc-Node-568" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">⇒</span></span></span></span></span><span id="MathJax-Element-45-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><mi>F</mi><mi>G</mi><mi>H</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>F</mi><mi>G</mi><mi>H</mi></math></span></span> là hình thoi (dấu hiệu nhận biết hình thoi).</p>
<p> </p>
<p> </p>
<p> </p>
<p> </p>
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