Ôn Tập Chương 1
Hướng dẫn giải Bài 89 (Trang 111 SGK Toán Hình học 8, Tập 1)
<p><strong class="content_question">Đề bài</strong></p>
<p>Cho tam giác <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></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></span></span> vuông tại <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></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></span></span>, đường trung tuyến <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>A</mi><mi>M</mi></math>"><span id="MJXc-Node-9" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-10" class="mjx-mrow"><span id="MJXc-Node-11" 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>M</mi></math></span></span>. Gọi <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>D</mi></math>"><span id="MJXc-Node-13" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-14" class="mjx-mrow"><span id="MJXc-Node-15" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span></span></span></span> là trung điểm của <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>B</mi><mo>,</mo><mi>E</mi></math>"><span id="MJXc-Node-16" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-17" class="mjx-mrow"><span id="MJXc-Node-18" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-19" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-20" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-21" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">E</span></span></span></span></span> là điểm đối xứng với <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>M</mi></math>"><span id="MJXc-Node-22" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-23" class="mjx-mrow"><span id="MJXc-Node-24" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">M</span></span></span></span></span> qua <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></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math></span></span>.</p>
<p>a) Chứng minh rằng điểm <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>E</mi></math>"><span id="MJXc-Node-28" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-29" class="mjx-mrow"><span id="MJXc-Node-30" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span></span></span></span> đối xứng với điểm <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>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> qua <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>A</mi><mi>B</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>B</mi></math></span></span>.</p>
<p>b) Các 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>E</mi><mi>M</mi><mi>C</mi><mo>,</mo><mi>A</mi><mi>E</mi><mi>B</mi><mi>M</mi></math>"><span id="MJXc-Node-38" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-39" class="mjx-mrow"><span id="MJXc-Node-40" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-41" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-42" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">M</span></span><span id="MJXc-Node-43" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-44" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-45" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-46" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-47" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-48" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">M</span></span></span></span></span> là hình gì? Vì sao?</p>
<p>c) Cho <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>B</mi><mi>C</mi><mo>=</mo><mn>4</mn><mi>c</mi><mi>m</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">B</span></span><span id="MJXc-Node-52" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-53" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-54" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">4</span></span><span id="MJXc-Node-55" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">c</span></span><span id="MJXc-Node-56" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">m</span></span></span></span></span>, tính chu vi tứ giác <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>E</mi><mi>B</mi><mi>M</mi></math>"><span id="MJXc-Node-57" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-58" class="mjx-mrow"><span id="MJXc-Node-59" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-60" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-61" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-62" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">M</span></span></span></span></span>.</p>
<p>d) Tam giác vuông <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><mi>C</mi></math>"><span id="MJXc-Node-63" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-64" class="mjx-mrow"><span id="MJXc-Node-65" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-66" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-67" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span></span></span></span>, có điều kiện gì thì <span id="MathJax-Element-15-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>B</mi><mi>M</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>E</mi><mi>B</mi><mi>M</mi></math></span></span> là hình vuông?</p>
<p><strong class="content_detail">Lời giải chi tiết</strong></p>
<p><img src="https://img.loigiaihay.com/picture/2019/0425/h179-bai-89-trang-111-sgk-toan-8-t1.jpg" alt="" /></p>
<p>a) Ta có <span id="MathJax-Element-16-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>B</mi><mo>=</mo><mi>M</mi><mi>C</mi></math>"><span id="MJXc-Node-74" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-75" class="mjx-mrow"><span id="MJXc-Node-76" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">M</span></span><span id="MJXc-Node-77" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-78" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-79" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">M</span></span><span id="MJXc-Node-80" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span></span></span></span> (vì <span id="MathJax-Element-17-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 trung điểm của <span id="MathJax-Element-18-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>C</mi></math>"><span id="MJXc-Node-84" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-85" class="mjx-mrow"><span id="MJXc-Node-86" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-87" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span></span></span></span>),</p>
<p><span id="MathJax-Element-19-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>D</mi><mo>=</mo><mi>D</mi><mi>A</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-90" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-91" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</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">D</span></span><span id="MJXc-Node-94" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span></span></span></span> (vì <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>D</mi></math>"><span id="MJXc-Node-95" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-96" class="mjx-mrow"><span id="MJXc-Node-97" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</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>A</mi><mi>B</mi></math>"><span id="MJXc-Node-98" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-99" class="mjx-mrow"><span id="MJXc-Node-100" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-101" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span></span></span></span>)</p>
<p>nên <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>M</mi><mi>D</mi></math>"><span id="MJXc-Node-102" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-103" class="mjx-mrow"><span id="MJXc-Node-104" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">M</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> là đường trung bình của <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"><mo>&#x2206;</mo><mi>A</mi><mi>B</mi><mi>C</mi></math>"><span id="MJXc-Node-106" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-107" class="mjx-mrow"><span id="MJXc-Node-108" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">Δ</span></span><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">B</span></span><span id="MJXc-Node-111" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span></span></span></span> (dấu hiệu nhận biết đường trung bình của tam giác) </p>
<p>Do đó <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mi>D</mi><mo>/</mo><mo>/</mo><mi>A</mi><mi>C</mi><mo>,</mo><mi>M</mi><mi>D</mi><mo>=</mo><mfrac><mrow><mi>A</mi><mo>⁢</mo><mi>C</mi></mrow><mn>2</mn></mfrac></math> (tính chất đường trung bình của tam giác)<br />Do <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi>A</mi><mo>⁢</mo><mi>C</mi><mo>⟂</mo><mi>A</mi><mo>⁢</mo><mi>B</mi></mstyle></math> (gt) nên <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi>M</mi><mo>⁢</mo><mi>D</mi><mo>⟂</mo><mi>A</mi><mo>⁢</mo><mi>B</mi></mstyle></math><br />vi E là điểm đối xứng với M qua D nên D là trung điểm của EM hay DE=EM</p>
<p>Do đó, AB là đường trung trực của ME (do <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi>A</mi><mo>⁢</mo><mi>B</mi><mo>⟂</mo><mi>M</mi><mo>⁢</mo><mi>E</mi></mstyle></math> tại D và DE=DM) nên E đối xưúng với M qua AB.<br />b) Ta có: EM//AC (do MD//AC)<br />và EM=AC (cùng bằng 2DM)<br />Suy ra AEMC là hình bình hành (dấu hiệu nhận biết hình bình hành)</p>
<p>Tứ giác AEBM có hai đường chéo cắt nhau tại trung điểm mỗi đường nên là hình bình hành.</p>
<p>Hình bình hành AEBM có <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi>A</mi><mo>⁢</mo><mi>B</mi><mo>⟂</mo><mi>E</mi><mo>⁢</mo><mi>M</mi></mstyle></math> (chứng minh trên) nên AEBM là hình thoi (dấu hiệu nhận biết hình thoi)<br />c) Ta có <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi>B</mi><mo>⁢</mo><mi>C</mi><mo>=</mo><mpadded><mn>4</mn></mpadded><mo>⁢</mo><mi>cm</mi><mo>⇒</mo><mi>B</mi><mo>⁢</mo><mi>M</mi><mo>=</mo><mpadded><mn>2</mn></mpadded><mo>⁢</mo><mi>cm</mi></mstyle></math> (do M là trung điểm BC)<br />Chu vi hình thoi AEBM bằng 4.BM=4.2=8(cm)</p>
<p>d) Cách 1 :<br />Hình thoi AEBM là hình vuông <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>⇔</mo><mi>A</mi><mi>B</mi><mo>=</mo><mi>E</mi><mi>M</mi><mo>⇔</mo><mi>A</mi><mi>B</mi><mo>=</mo><mi>A</mi><mi>C</mi></mstyle></math><br />Vậy nếu ABC vuông có thêm điều kiện AB=AC (tức là tam giác ABC vuông cân tại A) thì AEBM là hình vuông.</p>
<p>Cách 2 :</p>
<p>Hình thoi <span id="MathJax-Element-62-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>B</mi><mi>M</mi></math>"><span id="MJXc-Node-362" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-363" class="mjx-mrow"><span id="MJXc-Node-364" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-365" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-366" 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>M</mi></math></span></span> là hình vuông <span id="MathJax-Element-63-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">&#x21D4;</mo><mi>A</mi><mi>M</mi><mo>&#x22A5;</mo><mi>B</mi><mi>M</mi></math>"><span id="MJXc-Node-368" class="mjx-math" aria-hidden="true"><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 id="MJXc-Node-371" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-372" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">M</span></span><span id="MJXc-Node-373" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">⊥</span></span><span id="MJXc-Node-374" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-375" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">M</span></span></span></span></span></p>
<p><span id="MathJax-Element-64-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">&#x21D4;</mo><mo>&#x2206;</mo><mi>A</mi><mi>B</mi><mi>C</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">⇔</mo><mo>∆</mo><mi>A</mi><mi>B</mi><mi>C</mi></math></span></span> có trung tuyến <span id="MathJax-Element-65-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>M</mi></math>"><span id="MJXc-Node-383" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-384" class="mjx-mrow"><span id="MJXc-Node-385" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-386" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">M</span></span></span></span></span> là đường cao</p>
<p><span id="MathJax-Element-66-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">&#x21D4;</mo><mo>&#x2206;</mo><mi>A</mi><mi>B</mi><mi>C</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">⇔</mo><mo>∆</mo><mi>A</mi><mi>B</mi><mi>C</mi></math></span></span> cân tại <span id="MathJax-Element-67-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></math>"><span id="MJXc-Node-394" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-395" class="mjx-mrow"><span id="MJXc-Node-396" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span></span></span></span> (dấu hiệu nhận biết tam giác cân)</p>
<p>Vậy nếu <span id="MathJax-Element-68-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>B</mi><mi>C</mi></math>"><span id="MJXc-Node-397" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-398" class="mjx-mrow"><span id="MJXc-Node-399" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">Δ</span></span><span id="MJXc-Node-400" class="mjx-mi"><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">B</span></span><span id="MJXc-Node-402" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span></span></span></span> vuông có thêm điều kiện cân tại <span id="MathJax-Element-69-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></math>"><span id="MJXc-Node-403" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-404" class="mjx-mrow"><span id="MJXc-Node-405" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span></span></span></span> thì <span id="MathJax-Element-70-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>B</mi><mi>M</mi></math>"><span id="MJXc-Node-406" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-407" class="mjx-mrow"><span id="MJXc-Node-408" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-409" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-410" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-411" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">M</span></span></span></span></span> là hình vuông.</p>
<p> </p>
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