Bài 3: Diện Tích Tam Giác
Hướng dẫn giải Bài 20 (Trang 122 SGK Toán Hình học 8, Tập 1)
<p><strong class="content_question">Đề bài</strong></p>
<p>Vẽ hình chữ nhật có một cạnh bằng một cạnh của một tam giác cho trước và có diện tích bằng diện tích của tam giác đó. Từ đó suy ra một cách chứng minh khác về công thức tính diện tích tam giác.</p>
<p><strong class="content_detail">Lời giải chi tiết</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 class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>B</mi><mi>C</mi></math></span></span> với đường cao <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>H</mi></math>"><span id="MJXc-Node-6" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-7" class="mjx-mrow"><span id="MJXc-Node-8" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-9" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">H</span></span></span></span></span></p>
<p>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>M</mi><mo>,</mo><mi>N</mi><mo>,</mo><mi>I</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">M</span></span><span id="MJXc-Node-13" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-14" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">N</span></span><span id="MJXc-Node-15" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-16" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">I</span></span></span></span></span> 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>A</mi><mi>C</mi><mo>,</mo><mi>A</mi><mi>H</mi><mo>.</mo></math>"><span id="MJXc-Node-17" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-18" class="mjx-mrow"><span id="MJXc-Node-19" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-20" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-21" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-22" class="mjx-mi MJXc-space1"><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">C</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">A</span></span><span id="MJXc-Node-26" 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"><mo>.</mo></math></span></span></p>
<p>Lấy <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>E</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi></math></span></span> 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>I</mi></math>"><span id="MJXc-Node-31" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-32" class="mjx-mrow"><span id="MJXc-Node-33" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">I</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>M</mi><mo>,</mo><mi>D</mi></math>"><span id="MJXc-Node-34" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-35" class="mjx-mrow"><span id="MJXc-Node-36" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">M</span></span><span id="MJXc-Node-37" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-38" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">D</span></span></span></span></span> đối xứng với <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>I</mi></math>"><span id="MJXc-Node-39" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-40" class="mjx-mrow"><span id="MJXc-Node-41" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">I</span></span></span></span><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math></span></span> qua <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>N</mi><mo>.</mo></math>"><span id="MJXc-Node-42" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-43" class="mjx-mrow"><span id="MJXc-Node-44" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">N</span></span><span id="MJXc-Node-45" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">.</span></span></span></span></span></p>
<p><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"><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> Hình chữ nhật <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>B</mi><mi>E</mi><mi>D</mi><mi>C</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mi>E</mi><mi>D</mi><mi>C</mi></math></span></span> là hình cần dựng.</p>
<p><img src="https://img.loigiaihay.com/picture/2019/0416/h67-bai-20-trang-122-sgk-toan-8-t1_1.jpg" alt="" /></p>
<p>Thật vậy: </p>
<p>Vì <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: 400; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: 0px; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; color: #000000; font-family: OpenSans, Tahoma, Helvetica, sans-serif; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</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></span></span> đối xứng với <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: 400; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: 0px; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; color: #000000; font-family: OpenSans, Tahoma, Helvetica, sans-serif; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math>"><span id="MJXc-Node-58" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-59" class="mjx-mrow"><span id="MJXc-Node-60" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">I</span></span></span></span></span> qua <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: 400; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: 0px; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; color: #000000; font-family: OpenSans, Tahoma, Helvetica, sans-serif; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</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">M</span></span></span></span></span> nên <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: 400; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: 0px; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; color: #000000; font-family: OpenSans, Tahoma, Helvetica, sans-serif; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>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-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: 400; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: 0px; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; color: #000000; font-family: OpenSans, Tahoma, Helvetica, sans-serif; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>I</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">E</span></span><span id="MJXc-Node-70" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">I</span></span></span></span></span></p>
<p>Do đó, <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>E</mi><mi>M</mi><mo>=</mo><mi>M</mi><mi>I</mi></math>"><span id="MJXc-Node-71" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-72" class="mjx-mrow"><span id="MJXc-Node-73" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-74" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">M</span></span><span id="MJXc-Node-75" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-76" class="mjx-mi MJXc-space3"><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">I</span></span></span></span></span></p>
<p>Xét hai tam giác <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"><mo>&#x2206;</mo><mi>E</mi><mi>B</mi><mi>M</mi></math>"><span id="MJXc-Node-78" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-79" class="mjx-mrow"><span id="MJXc-Node-80" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">Δ</span></span><span id="MJXc-Node-81" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</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-mi"><span class="mjx-char MJXc-TeX-math-I">M</span></span></span></span></span> và <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"><mo>&#x2206;</mo><mi>I</mi><mi>A</mi><mi>M</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-mo"><span class="mjx-char MJXc-TeX-main-R">Δ</span></span><span id="MJXc-Node-87" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">I</span></span><span id="MJXc-Node-88" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-89" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">M</span></span></span></span></span> có:</p>
<p>+) MA=MB (do M là trung điểm của AB)<br />+) <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mover accent="true"><mrow><mi>B</mi><mo>⁢</mo><mi>M</mi><mo>⁢</mo><mi>E</mi></mrow><mo>^</mo></mover><mo>=</mo><mover accent="true"><mrow><mi>A</mi><mo>⁢</mo><mi>M</mi><mo>⁢</mo><mi>I</mi></mrow><mo>^</mo></mover></mstyle></math> (đối đỉnh)<br />+) EM=MI (chứng minh trên)<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>⇒</mo><mi mathvariant="normal">Δ</mi><mo>⁢</mo><mi>E</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>M</mi><mo>=</mo><mi mathvariant="normal">Δ</mi><mo>⁢</mo><mi>I</mi><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mi>M</mi><mo>⁢</mo><mrow><mo>(</mo><mi mathvariant="normal">c</mi><mo>-</mo><mi mathvariant="normal">g</mi><mo>-</mo><mi mathvariant="normal">c</mi><mo>)</mo></mrow></mstyle></math><br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>⇒</mo><msub><mi>S</mi><mrow><mi>I</mi><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mi>M</mi></mrow></msub><mo>=</mo><msub><mi>S</mi><mrow><mi>E</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>M</mi></mrow></msub></mstyle></math><br />Vì D đối xứng với I qua N nên N là trung điểm của DI<br />Do đó, NI=ND<br />Xét hai tam giác <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi mathvariant="normal">Δ</mi><mo>⁢</mo><mi>I</mi><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mi>N</mi></mstyle></math> và <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi mathvariant="normal">Δ</mi><mo>⁢</mo><mi>D</mi><mo>⁢</mo><mi>C</mi><mo>⁢</mo><mi>N</mi></mstyle></math> có:<br />+) IN=ND (chứng minh trên)<br />+) <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mover accent="true"><mrow><mi>A</mi><mo>⁢</mo><mi>N</mi><mo>⁢</mo><mi>I</mi></mrow><mo>^</mo></mover><mo>=</mo><mover accent="true"><mrow><mi>D</mi><mo>⁢</mo><mi>N</mi><mo>⁢</mo><mi>C</mi></mrow><mo>^</mo></mover></mstyle></math> (đối đỉnh)<br />+) AN=NC (do <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi mathvariant="normal">N</mi></mstyle></math> là trung điểm của <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi>AC</mi></mstyle></math>)<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>⇒</mo><mi mathvariant="normal">Δ</mi><mo>⁢</mo><mi>I</mi><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mi>N</mi><mo>=</mo><mi mathvariant="normal">Δ</mi><mo>⁢</mo><mi>D</mi><mo>⁢</mo><mi>C</mi><mo>⁢</mo><mi>N</mi></mstyle></math> (c-g-c)<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>⇒</mo><msub><mi>S</mi><mrow><mi>D</mi><mo>⁢</mo><mi>C</mi><mo>⁢</mo><mi>N</mi></mrow></msub><mo>=</mo><msub><mi>S</mi><mrow><mi>I</mi><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mi>N</mi></mrow></msub></mstyle></math><br />Ta có:<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><msub><mi>S</mi><mrow><mi>B</mi><mo>⁢</mo><mi>E</mi><mo>⁢</mo><mi>M</mi></mrow></msub><mo>+</mo><msub><mi>S</mi><mrow><mi>B</mi><mo>⁢</mo><mi>M</mi><mo>⁢</mo><mi>N</mi><mo>⁢</mo><mi>C</mi></mrow></msub><mo>+</mo><msub><mi>S</mi><mrow><mi>N</mi><mo>⁢</mo><mi>D</mi><mo>⁢</mo><mi>C</mi></mrow></msub><mo>=</mo><msub><mi>S</mi><mrow><mi>A</mi><mo>⁢</mo><mi>M</mi><mo>⁢</mo><mi>I</mi></mrow></msub><mo>+</mo><msub><mi>S</mi><mrow><mi>B</mi><mo>⁢</mo><mi>M</mi><mo>⁢</mo><mi>N</mi><mo>⁢</mo><mi>C</mi></mrow></msub><mo>+</mo><msub><mi>S</mi><mrow><mi>A</mi><mo>⁢</mo><mi>I</mi><mo>⁢</mo><mi>N</mi></mrow></msub></mstyle></math><br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mrow><mo>⇒</mo><msub><mi>S</mi><mrow><mi>A</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>C</mi></mrow></msub><mo>=</mo><msub><mi>S</mi><mrow><mi>E</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi mathvariant="normal">D</mi><mo>⁢</mo><mi>C</mi></mrow></msub><mo>=</mo><mi>B</mi><mo>⁢</mo><mi>E</mi></mrow><mo>.</mo><mi>B</mi><mo>⁢</mo><mi>C</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mi>H</mi><mo>.</mo><mi>B</mi><mo>⁢</mo><mi>C</mi></mstyle></math> (vì <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi>B</mi><mi>E</mi><mo>=</mo><mi>I</mi><mi>H</mi><mo>=</mo><mfrac><mrow><mi>A</mi><mo>⁢</mo><mi>H</mi></mrow><mn>2</mn></mfrac><mo>)</mo></mstyle></math></p>
<p>Ta đã tìm được công thức tính diện tích tam giác bằng một phương pháp khác.<br />Chú ý: Theo cách dựng trên ta có BEDC là hình chữ nhật vì:<br />+) <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi>MN</mi></mstyle></math> là đường trung bình của tam giác <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi>ABC</mi></mstyle></math> nên MN//BC hay ED//BC<br />+) Vi <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi mathvariant="normal">△</mi><mo>⁢</mo><mi>E</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>M</mi><mo>=</mo><mi mathvariant="normal">△</mi><mo>⁢</mo><mi>I</mi><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mi>M</mi></mstyle></math> nên <math xmlns="http://www.w3.org/1998/Math/MathML"><mover accent="true"><mrow><mi>E</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>M</mi></mrow><mo>^</mo></mover><mo>=</mo><mover accent="true"><mrow><mi>M</mi><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mi>I</mi></mrow><mo>^</mo></mover></math> mà hai góc này ở<br />vị trí so le trong nên EB//AI hay EB//AH<br />+) Vi <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi mathvariant="normal">△</mi><mo>⁢</mo><mi>I</mi><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mi>N</mi><mo>=</mo><mi mathvariant="normal">△</mi><mo>⁢</mo><mi>D</mi><mo>⁢</mo><mi>C</mi><mo>⁢</mo><mi>N</mi></mstyle></math> nên <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mover accent="true"><mrow><mi>D</mi><mo>⁢</mo><mi>C</mi><mo>⁢</mo><mi>N</mi></mrow><mo>^</mo></mover><mo>=</mo><mover accent="true"><mrow><mi>N</mi><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mi>I</mi></mrow><mo>^</mo></mover></mstyle></math> mà hai góc này ở<br />vị trí so le trong nên DC//AI<br />Do đó EB//DC và ED//BC nên BEDC là hình bình hành<br />Mà <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi>A</mi><mi>H</mi><mo>⟂</mo><mi>B</mi><mi>C</mi><mo>,</mo><mi>E</mi><mi>B</mi><mo>/</mo><mo>/</mo><mi>A</mi><mi>H</mi></mstyle></math> nên <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi>E</mi><mo>⁢</mo><mi>B</mi><mo>⟂</mo><mi>B</mi><mo>⁢</mo><mi>C</mi></mstyle></math>, suy ra BEDC là hình chữ nhật.</p>
<p><br /><br /></p>
<p> </p>
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