Bài 8. Các trường hợp đồng dạng của tam giác vuông
Hướng dẫn giải Bài 49 (Trang 84 SGK Toán Hình học 8, Tập 2)
<p>Ở hình 51, 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: 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>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"><mi>A</mi><mi>B</mi><mi>C</mi></math></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: 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>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> có đường cao <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: 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>A</mi><mi>H</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">AH</span></span></span></span></span></p>
<p><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: 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>A</mi><mi>H</mi></math>"><img class="wscnph" style="max-width: 100%;" src="https://static.colearn.vn:8413/v1.0/upload/library/25072022/7bc086ce-870b-4b11-8cba-2153c73b18ab.PNG" /></span></p>
<p><strong>LG a.</strong></p>
<p>Trong hình vẽ có bao nhiêu cặp tam giác đồng dạng?</p>
<p><strong>Phương pháp giải:</strong></p>
<p>Áp dụng:</p>
<p>- Trường hợp đồng dạng: Tam giác vuông này có một góc nhọn bằng góc nhọn của tam giác vuông kia. </p>
<p><strong>Lời giải chi tiết:</strong></p>
<p><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: 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>A</mi><mi>H</mi></math>"><br /><br /></span>Xét <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: 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"><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>∆</mo><mi>A</mi><mi>B</mi><mi>C</mi></math></span></span> và <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: 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"><mo>&#x2206;</mo><mi>H</mi><mi>B</mi><mi>A</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∆</mo><mi>H</mi><mi>B</mi><mi>A</mi></math></span></span> có:<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⁢</mo><mover accent="true"><mi>A</mi><mo>^</mo></mover><mo>=</mo><mover accent="true"><mi>H</mi><mo>^</mo></mover><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"><mover accent="true"><mi>B</mi><mo>^</mo></mover></mstyle></math> chung<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi mathvariant="normal">Δ</mi><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>C</mi><mo>⁢</mo><mo>~</mo><mo>⁢</mo><mi mathvariant="normal">Δ</mi><mo>⁢</mo><mi>H</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mo>⁢</mo><mrow><mo>(</mo><mi>g</mi><mo>-</mo><mi>g</mi><mo>)</mo></mrow><mo>⁢</mo></math><br />Xét <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi mathvariant="normal">△</mi><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>C</mi></mstyle></math> và <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi mathvariant="normal">△</mi><mo>⁢</mo><mi>H</mi><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mi>C</mi></mstyle></math> có:<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⁢</mo><mover accent="true"><mi>A</mi><mo>^</mo></mover><mo>=</mo><mover accent="true"><mi>H</mi><mo>^</mo></mover><mo>=</mo><msup><mn>90</mn><mo>∘</mo></msup></math><br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mover accent="true"><mi>C</mi><mo>^</mo></mover></mstyle></math> chung<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi mathvariant="normal">Δ</mi><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>C</mi><mo>⁢</mo><mo>~</mo><mo>⁢</mo><mi mathvariant="normal">Δ</mi><mo>⁢</mo><mi>H</mi><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mi>C</mi><mo>⁢</mo><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow><mo>⁢</mo><mrow><mo>(</mo><mi>g</mi><mo>-</mo><mi>g</mi><mo>)</mo></mrow><mo>⁢</mo></math><br />Từ' (1) và (2) suy ra <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi mathvariant="normal">Δ</mi><mo>⁢</mo><mi>H</mi><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mi>C</mi><mo>⁢</mo><mo>~</mo><mo>⁢</mo><mi mathvariant="normal">Δ</mi><mo>⁢</mo><mi>H</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>A</mi></mstyle></math> (vì cùng đồng dạng với <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi mathvariant="normal">Δ</mi><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>C</mi></mstyle></math>)</p>
<p>Vậy trong hình vẽ có 3 cặp tam giác đồng dạng</p>
<p><strong>LG b.</strong></p>
<p>Cho biết: <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>A</mi><mi>B</mi><mo>=</mo><mn>12</mn><mo>,</mo><mn>45</mn><mi>c</mi><mi>m</mi></math>"><span id="MJXc-Node-130" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-131" class="mjx-mrow"><span id="MJXc-Node-132" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-133" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-134" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-135" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">12</span></span><span id="MJXc-Node-136" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-137" class="mjx-mn MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">45</span></span><span id="MJXc-Node-138" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">c</span></span><span id="MJXc-Node-139" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">m</span></span></span></span></span>, <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>A</mi><mi>C</mi><mo>=</mo><mn>20</mn><mo>,</mo><mn>50</mn><mi>c</mi><mi>m</mi></math>"><span id="MJXc-Node-140" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-141" class="mjx-mrow"><span id="MJXc-Node-142" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-143" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-144" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-145" class="mjx-mn MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">20</span></span><span id="MJXc-Node-146" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-147" class="mjx-mn MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">50</span></span><span id="MJXc-Node-148" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">c</span></span><span id="MJXc-Node-149" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">m</span></span></span></span></span>. Tính độ dài các đoạn <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><mo>,</mo><mi>A</mi><mi>H</mi><mo>,</mo><mi>B</mi><mi>H</mi></math>"><span id="MJXc-Node-150" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-151" class="mjx-mrow"><span id="MJXc-Node-152" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-153" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-154" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-155" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-156" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">H</span></span><span id="MJXc-Node-157" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-158" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-159" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">H</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"><mi>C</mi><mi>H</mi><mo>.</mo></math>"><span id="MJXc-Node-160" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-161" class="mjx-mrow"><span id="MJXc-Node-162" 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>H</mi><mo>.</mo></math></span></span></p>
<p><strong>Phương pháp giải:</strong></p>
<p>Áp dụng:</p>
<p>- Tính chất hai tam giác đồng dạng và định lý Pytago</p>
<p><strong>Lời giải chi tiết:</strong></p>
<p><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"><mo>&#x2206;</mo><mi>A</mi><mi>B</mi><mi>C</mi></math>"><span id="MJXc-Node-165" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-166" class="mjx-mrow"><span id="MJXc-Node-167" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">Δ</span></span><span id="MJXc-Node-168" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-169" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-170" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span></span></span></span> vuông tại <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></math>"><span id="MJXc-Node-171" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-172" class="mjx-mrow"><span id="MJXc-Node-173" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span></span></span></span> (giả thiết) nên áp dụng định lí Pitago ta có:</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><msup><mi>C</mi><mn>2</mn></msup><mo>=</mo><mi>A</mi><msup><mi>B</mi><mn>2</mn></msup><mo>+</mo><mi>A</mi><mpadded><msup><mi>C</mi><mn>2</mn></msup></mpadded><mspace linebreak="newline"/><mo> </mo><mo> </mo><mo mathvariant="italic"> </mo><mo>=</mo><mn>12</mn><mo>,</mo><msup><mn>45</mn><mn>2</mn></msup><mo>+</mo><mn>20</mn><mo>,</mo><msup><mn>50</mn><mn>2</mn></msup><mo>=</mo><mn>575</mn><mo>,</mo><mpadded><mn>2525</mn></mpadded><mspace linebreak="newline"/><mo>⇒</mo><mi>B</mi><mi>C</mi><mo>=</mo><msqrt><mn>575</mn><mo>,</mo><mn>2525</mn></msqrt><mo>≈</mo><mpadded><mn>24</mn></mpadded><mi>cm</mi></math><br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mi mathvariant="normal">△</mi><mo>⁢</mo><mi>A</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>C</mi><mo>⁢</mo><mo>~</mo><mo>⁢</mo><mi mathvariant="normal">△</mi><mo>⁢</mo><mi>H</mi><mo>⁢</mo><mi>B</mi><mo>⁢</mo><mi>A</mi></mstyle></math> (chứng minh trên)<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mfrac><mrow><mi>A</mi><mo>⁢</mo><mi>B</mi></mrow><mrow><mi>H</mi><mo>⁢</mo><mi>B</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>B</mi><mo>⁢</mo><mi>C</mi></mrow><mrow><mi>B</mi><mo>⁢</mo><mi>A</mi></mrow></mfrac><mo> </mo><mrow><mo>(</mo><mi>c</mi><mi>ặ</mi><mi>p</mi><mo> </mo><mi>cạnh</mi><mo> </mo><mi>tương</mi><mo> </mo><mi>ứ</mi><mi>n</mi><mi>g</mi><mo> </mo><mi>t</mi><mi>ỉ</mi><mo> </mo><mi>lệ</mi><mo>)</mo></mrow><mspace linebreak="newline"/><mo>⇒</mo><mi>H</mi><mi>B</mi><mo>=</mo><mfrac><mrow><mi>A</mi><mo>⁢</mo><msup><mi>B</mi><mn>2</mn></msup></mrow><mrow><mi>B</mi><mo>⁢</mo><mi>C</mi></mrow></mfrac><mo>≈</mo><mfrac><mrow><mn>12</mn><mo>,</mo><msup><mn>45</mn><mn>2</mn></msup></mrow><mn>24</mn></mfrac><mo>≈</mo><mn>6</mn><mo>,</mo><mpadded><mn>5</mn></mpadded><mpadded><mi>cm</mi></mpadded><mspace linebreak="newline"/><mo>⇒</mo><mi>C</mi><mi>H</mi><mo>=</mo><mi>B</mi><mi>C</mi><mo>-</mo><mi>B</mi><mi>H</mi><mo>≈</mo><mn>24</mn><mo>-</mo><mn>6</mn><mo>,</mo><mn>5</mn><mo>=</mo><mn>17</mn><mo>,</mo><mpadded><mn>5</mn></mpadded><mi>cm</mi><mo>.</mo><mi mathvariant="normal">&</mi><mspace linebreak="newline"/><mi>M</mi><mi>ặ</mi><mi>t</mi><mo> </mo><mi>k</mi><mi>h</mi><mi>á</mi><mi>c</mi><mo>:</mo><mfrac><mrow><mi>A</mi><mo>⁢</mo><mi>C</mi></mrow><mrow><mi>A</mi><mo>⁢</mo><mi>H</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>B</mi><mo>⁢</mo><mi>C</mi></mrow><mrow><mi>B</mi><mo>⁢</mo><mi>A</mi></mrow></mfrac><mo> </mo><mrow><mo>(</mo><mi>d</mi><mi>o</mi><mo> </mo><mi mathvariant="normal">Δ</mi><mi>A</mi><mi>B</mi><mi>C</mi><mo>~</mo><mi mathvariant="normal">Δ</mi><mi>H</mi><mi>B</mi><mi>A</mi><mo> </mo><mi>t</mi><mi>h</mi><mi>e</mi><mi>o</mi><mo> </mo><mi>c</mi><mi>â</mi><mi>u</mi><mo> </mo><mi>a</mi><mo>)</mo></mrow><mspace linebreak="newline"/><mo>⇒</mo><mi>A</mi><mi>H</mi><mo>=</mo><mfrac><mrow><mi>A</mi><mo>⁢</mo><mi>B</mi><mo>.</mo><mi>A</mi><mo>⁢</mo><mi>C</mi></mrow><mrow><mi>B</mi><mo>⁢</mo><mi>C</mi></mrow></mfrac><mo>≈</mo><mpadded><mfrac><mrow><mn>12</mn><mo>,</mo><mn>45.20</mn><mo>,</mo><mn>50</mn></mrow><mn>24</mn></mfrac></mpadded><mspace linebreak="newline"/><mo>⇒</mo><mi>A</mi><mi>H</mi><mo>≈</mo><mn>10</mn><mo>,</mo><mpadded><mn>6</mn></mpadded><mi>cm</mi><mo>.</mo></math></p>
<p> </p>
<p> </p>
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