Bài 12: Hình Vuông
Hướng dẫn giải Bài 85 (Trang 109 SGK Toán Hình học 8, Tập 1)
<p><strong class="content_question">Đề bài</strong></p>
<p>Cho hình chữ nhật <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> có <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>=</mo><mn>2</mn><mi>A</mi><mi>D</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-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">2</span></span><span id="MJXc-Node-13" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-14" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span></span></span></span>. Gọi <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>E</mi><mo>,</mo><mi>F</mi></math>"><span id="MJXc-Node-15" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-16" class="mjx-mrow"><span id="MJXc-Node-17" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-18" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-19" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">F</span></span></span></span></span> theo thứ tự là trung điểm của <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><mo>,</mo><mi>C</mi><mi>D</mi></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">A</span></span><span id="MJXc-Node-23" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-24" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-25" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-26" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span></span></span></span>. Gọi <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>M</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math></span></span> là giao điểm của <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>A</mi><mi>F</mi></math>"><span id="MJXc-Node-30" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-31" class="mjx-mrow"><span id="MJXc-Node-32" 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>F</mi></math></span></span> và <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>D</mi><mi>E</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mi>E</mi></math></span></span>, <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>N</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math></span></span> là giao điểm của <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>B</mi><mi>F</mi></math>"><span id="MJXc-Node-41" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-42" class="mjx-mrow"><span id="MJXc-Node-43" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span></span></span><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math></span></span> và <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>C</mi><mi>E</mi></math>"><span id="MJXc-Node-45" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-46" class="mjx-mrow"><span id="MJXc-Node-47" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-48" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span></span></span></span>.</p>
<p>a) Tứ giác <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><mi>D</mi><mi>F</mi><mi>E</mi></math>"><span id="MJXc-Node-49" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-50" class="mjx-mrow"><span id="MJXc-Node-51" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-52" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span><span id="MJXc-Node-53" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span><span id="MJXc-Node-54" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span></span></span></span> là hình gì? Vì sao?</p>
<p>b) Tứ giác <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>E</mi><mi>M</mi><mi>F</mi><mi>N</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">E</span></span><span id="MJXc-Node-58" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">M</span></span><span id="MJXc-Node-59" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span><span id="MJXc-Node-60" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">N</span></span></span></span></span> là hình gì? Vì sao?</p>
<p><strong class="content_detail">Lời giải chi tiết</strong></p>
<p><img src="https://img.loigiaihay.com/picture/2018/0713/b85-trang-109-sgk-toan-8-t-1-c2.jpg" alt="" /></p>
<p>Vì <span id="MathJax-Element-13-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-61" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-62" class="mjx-mrow"><span id="MJXc-Node-63" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-64" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-65" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-66" 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-14-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>=</mo><mi>C</mi><mi>D</mi><mo>,</mo><mi>A</mi><mi>D</mi><mo>=</mo><mi>B</mi><mi>C</mi><mo>,</mo><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-67" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-68" class="mjx-mrow"><span id="MJXc-Node-69" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-70" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-71" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-72" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-73" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span><span id="MJXc-Node-74" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-75" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-76" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span><span id="MJXc-Node-77" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-78" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-79" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-80" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-81" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-82" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-83" class="mjx-texatom"><span id="MJXc-Node-84" class="mjx-mrow"><span id="MJXc-Node-85" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-86" class="mjx-texatom"><span id="MJXc-Node-87" class="mjx-mrow"><span id="MJXc-Node-88" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-89" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-90" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span></span></span></span></p>
<p>Lại có E, F theo thứ tự là trung điểm của AB, CD nên <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><mi>E</mi><mo>⁢</mo><mi>B</mi><mo>=</mo><mfrac><mrow><mi>A</mi><mo>⁢</mo><mi>B</mi></mrow><mn>2</mn></mfrac><mo>,</mo><mi>D</mi><mo>⁢</mo><mi>F</mi><mo>=</mo><mi>F</mi><mo>⁢</mo><mi>C</mi><mo>=</mo><mfrac><mrow><mi>D</mi><mo>⁢</mo><mi>C</mi></mrow><mn>2</mn></mfrac></math><br />Lại có AB=2AD<br />Suy ra AE=EB=BC=CF=FD=DA<br />a) Xét tứ giác ADFE có:<br />AE//DF (do AB//CD), AE=DF (chứng minh trên)<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>⇒</mo></mstyle></math> Tứ giác ADFE là hình bình hành (dấu hiệu nhận biết hình bình hành)</p>
<p>Hình bình hành ADFE có <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>90</mn><mn>0</mn></msup></mstyle></math> nên là hình chữ nhật (dấu hiệu nhận biết hình chữ nhật )</p>
<p>Hình chữ nhật ADFE có AE=AD (chứng minh trên) nên nó là hình vuông (dấu hiệu nhận biết hình vuông)<br />b) Xét tứ giác DEBF có:<br />EB//DF (do AB//CD), EB=DF (chứng minh trên)<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>⇒</mo></mstyle></math> Tứ giác DEBF là hình bình hành (dấu hiệu nhận biết hình bình hành).<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>⇒</mo><mi>D</mi><mi>E</mi><mo>/</mo><mo>/</mo><mi>B</mi><mi>F</mi></mstyle></math> (tính chất hình bình hành)<br />Xét tứ giác AECF có:<br />EA//CF (do AB//CD), EA=CF (chứng minh trên)</p>
<p><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"><mo stretchy="false">&#x21D2;</mo></math>"><span id="MJXc-Node-334" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-335" class="mjx-mrow"><span id="MJXc-Node-336" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">⇒</span></span></span></span></span> Tứ giác <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"><mi>A</mi><mi>E</mi><mi>C</mi><mi>F</mi></math>"><span id="MJXc-Node-337" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-338" class="mjx-mrow"><span id="MJXc-Node-339" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-340" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-341" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-342" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span></span></span></span> là hình bình hành (dấu hiệu nhận biết hình bình hành).</p>
<p><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"><mo stretchy="false">&#x21D2;</mo></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">⇒</mo></math></span></span> <span id="MathJax-Element-46-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>F</mi><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>E</mi><mi>C</mi></math>"><span id="MJXc-Node-346" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-347" class="mjx-mrow"><span id="MJXc-Node-348" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-349" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span><span id="MJXc-Node-350" class="mjx-texatom"><span id="MJXc-Node-351" class="mjx-mrow"><span id="MJXc-Node-352" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-353" class="mjx-texatom"><span id="MJXc-Node-354" class="mjx-mrow"><span id="MJXc-Node-355" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-356" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-357" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span></span></span></span> (tính chất hình bình hành)</p>
<p>Xét tứ giác <span id="MathJax-Element-47-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>M</mi><mi>F</mi><mi>N</mi></math>"><span id="MJXc-Node-358" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-359" class="mjx-mrow"><span id="MJXc-Node-360" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-361" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">M</span></span><span id="MJXc-Node-362" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span><span id="MJXc-Node-363" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">N</span></span></span></span></span> có: <span id="MathJax-Element-48-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>M</mi><mi>E</mi><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>N</mi><mi>F</mi><mo>,</mo><mi>M</mi><mi>F</mi><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>N</mi><mi>E</mi></math>"><span id="MJXc-Node-364" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-365" class="mjx-mrow"><span id="MJXc-Node-366" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">M</span></span><span id="MJXc-Node-367" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-368" class="mjx-texatom"><span id="MJXc-Node-369" class="mjx-mrow"><span id="MJXc-Node-370" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-371" class="mjx-texatom"><span id="MJXc-Node-372" class="mjx-mrow"><span id="MJXc-Node-373" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-374" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">N</span></span><span id="MJXc-Node-375" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span><span id="MJXc-Node-376" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-377" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">M</span></span><span id="MJXc-Node-378" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span><span id="MJXc-Node-379" class="mjx-texatom"><span id="MJXc-Node-380" class="mjx-mrow"><span id="MJXc-Node-381" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-382" class="mjx-texatom"><span id="MJXc-Node-383" class="mjx-mrow"><span id="MJXc-Node-384" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-385" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">N</span></span><span id="MJXc-Node-386" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span></span></span></span> (do <span id="MathJax-Element-49-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><mo>,</mo><mi>A</mi><mi>F</mi><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>E</mi><mi>C</mi></math>"><span id="MJXc-Node-387" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-388" class="mjx-mrow"><span id="MJXc-Node-389" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span><span id="MJXc-Node-390" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-391" class="mjx-texatom"><span id="MJXc-Node-392" class="mjx-mrow"><span id="MJXc-Node-393" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-394" class="mjx-texatom"><span id="MJXc-Node-395" class="mjx-mrow"><span id="MJXc-Node-396" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-397" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-398" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span><span id="MJXc-Node-399" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-400" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-401" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span><span id="MJXc-Node-402" class="mjx-texatom"><span id="MJXc-Node-403" class="mjx-mrow"><span id="MJXc-Node-404" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-405" class="mjx-texatom"><span id="MJXc-Node-406" class="mjx-mrow"><span id="MJXc-Node-407" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-408" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-409" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span></span></span></span> (chứng minh trên))</p>
<p><span id="MathJax-Element-50-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-410" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-411" class="mjx-mrow"><span id="MJXc-Node-412" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">⇒</span></span></span></span></span> Tứ giác <span id="MathJax-Element-51-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>M</mi><mi>F</mi><mi>N</mi></math>"><span id="MJXc-Node-413" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-414" class="mjx-mrow"><span id="MJXc-Node-415" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-416" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">M</span></span><span id="MJXc-Node-417" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span><span id="MJXc-Node-418" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">N</span></span></span></span></span> là hình bình hành (dấu hiệu nhận biết hình bình hành).</p>
<p>Theo câu a, <span id="MathJax-Element-52-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><mi>F</mi><mi>E</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>D</mi><mi>F</mi><mi>E</mi></math></span></span> là hình vuông nên <span id="MathJax-Element-53-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>M</mi><mi>E</mi><mo>=</mo><mi>M</mi><mi>F</mi><mo>,</mo><mi>M</mi><mi>E</mi><mo>&#x22A5;</mo><mi>M</mi><mi>F</mi></math>"><span id="MJXc-Node-425" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-426" class="mjx-mrow"><span id="MJXc-Node-427" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">M</span></span><span id="MJXc-Node-428" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-429" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-430" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">M</span></span><span id="MJXc-Node-431" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span><span id="MJXc-Node-432" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-433" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">M</span></span><span id="MJXc-Node-434" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-435" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">⊥</span></span><span id="MJXc-Node-436" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">M</span></span><span id="MJXc-Node-437" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span></span></span></span> (tính chất hình vuông)</p>
<p>Hình bình hành EMFN có <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mover accent="true"><mi>M</mi><mo>^</mo></mover><mo>=</mo><msup><mn>90</mn><mn>0</mn></msup></mstyle></math> nên là hình chữ nhật, lại có ME=MF nên là hình vuông (dấu hiệu nhận biết hình vuông)<br /><br /><br /></p>
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