Bài 12: Hình Vuông
Hướng dẫn giải Bài 82 (Trang 108 SGK Toán Hình học 8, Tập 1)
<p><strong class="content_question">Đề bài</strong></p>
<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: 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>107</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">107</span></span></span></span><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>107</mn></math></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: 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-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 class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>B</mi><mi>C</mi><mi>D</mi></math></span></span> là hình vuông. Chứng minh rằng tứ giác <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><mi>F</mi><mi>G</mi><mi>H</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">E</span></span><span id="MJXc-Node-13" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span><span id="MJXc-Node-14" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">G</span></span><span id="MJXc-Node-15" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">H</span></span></span></span><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 vuông. </p>
<p><img src="https://img.loigiaihay.com/picture/2018/0713/b82-trang-108-sgk-toan-8-t-1-c2.jpg" alt="" width="281" height="386" data-adbro-processed="true" /></p>
<p><strong class="content_detail">Lời giải chi tiết</strong></p>
<p>Các tam giác vuông <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>E</mi><mi>H</mi><mo>,</mo><mi>B</mi><mi>F</mi><mi>E</mi><mo>,</mo><mi>C</mi><mi>G</mi><mi>F</mi><mo>,</mo><mi>D</mi><mi>H</mi><mi>G</mi></math>"><span id="MJXc-Node-19" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-20" class="mjx-mrow"><span id="MJXc-Node-21" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-22" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-23" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">H</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">B</span></span><span id="MJXc-Node-26" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span><span id="MJXc-Node-27" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-28" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-29" class="mjx-mi MJXc-space1"><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">G</span></span><span id="MJXc-Node-31" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span><span id="MJXc-Node-32" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-33" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">D</span></span><span id="MJXc-Node-34" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">H</span></span><span id="MJXc-Node-35" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">G</span></span></span></span></span> có:</p>
<p><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>E</mi><mo>=</mo><mi>B</mi><mi>F</mi><mo>=</mo><mi>C</mi><mi>G</mi><mo>=</mo><mi>D</mi><mi>H</mi></math>"><span id="MJXc-Node-36" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-37" class="mjx-mrow"><span id="MJXc-Node-38" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-39" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-40" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-41" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-42" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span><span id="MJXc-Node-43" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-44" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-45" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">G</span></span><span id="MJXc-Node-46" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-47" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">D</span></span><span id="MJXc-Node-48" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">H</span></span></span></span></span> (1) (giả thiết)</p>
<p>Theo giả thiết <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-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></span><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mi>C</mi><mi>D</mi></math></span></span> là hình vuông nên <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><mo>=</mo><mi>B</mi><mi>C</mi><mo>=</mo><mi>C</mi><mi>D</mi><mo>=</mo><mi>D</mi><mi>A</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-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-60" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-61" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-62" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-63" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-64" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span><span id="MJXc-Node-65" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-66" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">D</span></span><span id="MJXc-Node-67" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span></span></span></span> (2) (tính chất hình vuông)</p>
<p>Mà: <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>A</mi><mi>H</mi><mo>=</mo><mi>A</mi><mi>D</mi><mo>&#x2212;</mo><mi>D</mi><mi>H</mi><mo>,</mo><mi>B</mi><mi>E</mi><mo>=</mo><mi>A</mi><mi>B</mi><mo>&#x2212;</mo><mi>A</mi><mi>E</mi><mo>,</mo></math>"><span id="MJXc-Node-68" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-69" class="mjx-mrow"><span id="MJXc-Node-70" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-71" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">H</span></span><span id="MJXc-Node-72" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-73" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-74" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span><span id="MJXc-Node-75" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">−</span></span><span id="MJXc-Node-76" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">D</span></span><span id="MJXc-Node-77" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">H</span></span><span id="MJXc-Node-78" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-79" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-80" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-81" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-82" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-83" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-84" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">−</span></span><span id="MJXc-Node-85" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-86" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-87" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">, C</span></span></span></span></span><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>F</mi><mo>=</mo><mi>B</mi><mi>C</mi><mo>&#x2212;</mo><mi>B</mi><mi>F</mi><mo>,</mo><mi>D</mi><mi>G</mi><mo>=</mo><mi>D</mi><mi>C</mi><mo>&#x2212;</mo><mi>C</mi><mi>G</mi></math>"><span id="MJXc-Node-88" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-89" class="mjx-mrow"><span id="MJXc-Node-91" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span><span id="MJXc-Node-92" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-93" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-94" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-95" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">−</span></span><span id="MJXc-Node-96" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-97" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span><span id="MJXc-Node-98" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-99" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">D</span></span><span id="MJXc-Node-100" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">G</span></span><span id="MJXc-Node-101" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-102" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">D</span></span><span id="MJXc-Node-103" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-104" class="mjx-mo MJXc-space2"><span class="mjx-char MJXc-TeX-main-R">−</span></span><span id="MJXc-Node-105" class="mjx-mi MJXc-space2"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-106" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">G</span></span></span></span></span> (3)</p>
<p>Từ (1), (2) và (3) suy ra <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>H</mi><mo>=</mo><mi>B</mi><mi>E</mi><mo>=</mo><mi>C</mi><mi>F</mi><mo>=</mo><mi>D</mi><mi>G</mi></math>"><span id="MJXc-Node-107" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-108" class="mjx-mrow"><span id="MJXc-Node-109" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-110" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">H</span></span><span id="MJXc-Node-111" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-112" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-113" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-114" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-115" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-116" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span><span id="MJXc-Node-117" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-118" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">D</span></span><span id="MJXc-Node-119" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">G</span></span></span></span></span></p>
<p>Suy ra <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"><mo>&#x2206;</mo><mi>A</mi><mi>E</mi><mi>H</mi><mo>=</mo><mo>&#x2206;</mo><mi>B</mi><mi>F</mi><mi>E</mi><mo>=</mo><mo>&#x2206;</mo><mi>C</mi><mi>G</mi><mi>F</mi></math>"><span id="MJXc-Node-120" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-121" class="mjx-mrow"><span id="MJXc-Node-122" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">Δ</span></span><span id="MJXc-Node-123" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-124" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-125" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">H</span></span><span id="MJXc-Node-126" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-127" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">Δ</span></span><span id="MJXc-Node-128" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-129" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span><span id="MJXc-Node-130" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-131" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-132" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">Δ</span></span><span id="MJXc-Node-133" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-134" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">G</span></span><span id="MJXc-Node-135" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span></span></span></span><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"><mo>=</mo><mo>&#x2206;</mo><mi>D</mi><mi>H</mi><mi>G</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>∆</mo><mi>D</mi><mi>H</mi><mi>G</mi></math></span></span> (hai cạnh góc vuông)</p>
<p>Do đó</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mover accent="true"><mrow><mi>E</mi><mo></mo><mi>H</mi><mo></mo><mi>A</mi></mrow><mo>^</mo></mover><mo>=</mo><mover accent="true"><mrow><mi>F</mi><mo></mo><mi>E</mi><mo></mo><mi>B</mi></mrow><mo>^</mo></mover></mstyle></math> (4) (hai góc tương ứng bằng nhau)<br />HE=EF=FG=GH ( các cạnh tương ứng)<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>⇒</mo></mstyle></math> Tứ giác EFGH là hình thoi (dấu hiệu nhận biết hình thoi)<br />Xét tam giác AHE vuông tại A nên <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mover accent="true"><mrow><mi>H</mi><mo></mo><mi>E</mi><mo></mo><mi>A</mi></mrow><mo>^</mo></mover><mo>+</mo><mover accent="true"><mrow><mi>E</mi><mo></mo><mi>H</mi><mo></mo><mi>A</mi></mrow><mo>^</mo></mover><mo>=</mo><msup><mn>90</mn><mo>∘</mo></msup></mstyle></math><br />Ta có:<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mover accent="true"><mrow><mi>H</mi><mo></mo><mi>E</mi><mo></mo><mi>F</mi></mrow><mo>^</mo></mover><mo>+</mo><mover accent="true"><mrow><mi>H</mi><mo></mo><mi>E</mi><mo></mo><mi>A</mi></mrow><mo>^</mo></mover><mo>+</mo><mover accent="true"><mrow><mi>F</mi><mo></mo><mi>E</mi><mo></mo><mi>B</mi></mrow><mo>^</mo></mover><mo>=</mo><msup><mn>180</mn><mn>0</mn></msup></mstyle></math><br />Kết hợp với (4) và (5), ta có:<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mover accent="true"><mrow><mi>H</mi><mo></mo><mi>E</mi><mo></mo><mi>F</mi></mrow><mo>^</mo></mover><mo></mo><mo>=</mo><msup><mn>180</mn><mo>∘</mo></msup><mo>-</mo><mrow><mo>(</mo><mover accent="true"><mrow><mi>H</mi><mo></mo><mi>E</mi><mo></mo><mi>A</mi></mrow><mo>^</mo></mover><mo>+</mo><mover accent="true"><mrow><mi>F</mi><mo></mo><mi>E</mi><mo></mo><mi>B</mi></mrow><mo>^</mo></mover><mo>)</mo></mrow><mo></mo><mspace linebreak="newline"></mspace><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo>=</mo><msup><mn>180</mn><mo>∘</mo></msup><mo>-</mo><mrow><mo>(</mo><mover accent="true"><mrow><mi>H</mi><mo></mo><mi>E</mi><mo></mo><mi>A</mi></mrow><mo>^</mo></mover><mo>+</mo><mover accent="true"><mrow><mi>E</mi><mo></mo><mi>H</mi><mo></mo><mi>A</mi></mrow><mo>^</mo></mover><mo>)</mo></mrow><mo></mo><mspace linebreak="newline"></mspace><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo>=</mo><msup><mn>180</mn><mo>∘</mo></msup><mo>-</mo><msup><mn>90</mn><mn>0</mn></msup><mo>=</mo><msup><mn>90</mn><mo>∘</mo></msup><mo></mo></math><br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>⇒</mo></mstyle></math> Hình thoi EFGH là hình vuông (dấu hiệu nhận biết hình vuông)</p>
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