Bài 2: Định Lí Đảo Và Hệ Quả Của Định Lí Ta-Lét
Hướng dẫn giải Bài 13 (Trang 64 SGK Toán Hình học 8, Tập 2)
<p><strong class="content_question">Đề bài</strong></p>
<p>Có thể đo gián tiếp chiều cao của một bức tường bằng dụng cụ đo đơn giản được không?</p>
<p>Hình 19: thể hiện cách đo chiều cao <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></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> của một bức tường bằng các dụng cụ đơn giản gồm:</p>
<p>Hai cọc thẳng đứng và sợi dây <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>F</mi><mi>C</mi></math>"><span id="MJXc-Node-5" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-6" class="mjx-mrow"><span id="MJXc-Node-7" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span></span></span><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math></span></span>, Cọc 1 có chiều 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>D</mi><mi>K</mi><mo>=</mo><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">D</span></span><span id="MJXc-Node-12" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">K</span></span><span id="MJXc-Node-13" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-14" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">h</span></span></span></span></span>. Các khoảng cách <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"><mi>B</mi><mi>C</mi><mo>=</mo><mi>a</mi><mo>,</mo><mi>D</mi><mi>C</mi><mo>=</mo><mi>b</mi></math>"><span id="MJXc-Node-15" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-16" class="mjx-mrow"><span id="MJXc-Node-17" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-18" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-19" class="mjx-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-20" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">a</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">D</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 MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-25" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">b</span></span></span></span></span> đo được bằng thước thông dụng.</p>
<p>a) Em hãy cho biết người ta tiến hành đo đạc như thế nào ? </p>
<p>b) Tính chiều cao <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></math>"><span id="MJXc-Node-26" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-27" class="mjx-mrow"><span id="MJXc-Node-28" 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></math></span></span> theo <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>h</mi><mo>,</mo><mi>a</mi><mo>,</mo><mi>b</mi></math>"><span id="MJXc-Node-30" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-31" class="mjx-mrow"><span id="MJXc-Node-32" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">h</span></span><span id="MJXc-Node-33" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-34" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">a</span></span><span id="MJXc-Node-35" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-36" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">b</span></span></span></span></span>.</p>
<p><img src="https://img.loigiaihay.com/picture/2018/0718/b13-trang-64-sgk-toan-8-t2-c2.jpg" /><br /><br /></p>
<p><strong class="content_detail">Lời giải chi tiết</strong></p>
<p>a) Cách tiến hành:</p>
<p>- Đặt hai cọc thẳng đứng, di chuyển cọc <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"><mn>2</mn></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></span></span> sao cho <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"><mn>3</mn></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></span></span> 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>A</mi><mo>,</mo><mi>F</mi><mo>,</mo><mi>K</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>,</mo><mi>F</mi><mo>,</mo><mi>K</mi></math></span></span> nằm trên một đường thẳng.</p>
<p>- Dùng sợi dây căng thẳng 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"><mn>2</mn></math>"><span id="MJXc-Node-50" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-51" class="mjx-mrow"><span id="MJXc-Node-52" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">2</span></span></span></span></span> điểm <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>F</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math></span></span> và <span id="MathJax-Element-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>K</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>K</mi></math></span></span> để xác định điểm <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>C</mi></math>"><span id="MJXc-Node-59" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-60" class="mjx-mrow"><span id="MJXc-Node-61" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span></span></span></span> trên mặt đất (<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"><mn>3</mn></math>"><span id="MJXc-Node-62" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-63" class="mjx-mrow"><span id="MJXc-Node-64" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">3</span></span></span></span></span> điểm <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>F</mi><mo>,</mo><mi>K</mi><mo>,</mo><mi>C</mi></math>"><span id="MJXc-Node-65" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-66" class="mjx-mrow"><span id="MJXc-Node-67" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span><span id="MJXc-Node-68" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-69" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">K</span></span><span id="MJXc-Node-70" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-71" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">C</span></span></span></span></span> thẳng hàng).</p>
<p>b) <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> có AB//DK nên <math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mfrac><mrow><mi>D</mi><mo>⁢</mo><mi>K</mi></mrow><mrow><mi>A</mi><mo>⁢</mo><mi>B</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>D</mi><mo>⁢</mo><mi>C</mi></mrow><mrow><mi>B</mi><mo>⁢</mo><mi>C</mi></mrow></mfrac></mstyle></math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>⇒</mo><mi>A</mi><mo>⁢</mo><mi>B</mi><mo>=</mo><mfrac><mrow><mi>D</mi><mo>⁢</mo><mi>K</mi><mo>⋅</mo><mi>B</mi><mo>⁢</mo><mi>C</mi></mrow><mrow><mi>D</mi><mo>⁢</mo><mi>C</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>h</mi><mo>⋅</mo><mi>a</mi></mrow><mi>b</mi></mfrac></mstyle></math> (theo hệ quả định lí Talet)</p>
<p>Vậy chiều cao của bức tường <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>⁢</mo><mi>B</mi><mo>=</mo><mfrac><mrow><mi>h</mi><mo>⋅</mo><mi>a</mi></mrow><mi>b</mi></mfrac><mo>.</mo></math></p>
<p> </p>
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<p><br /><br /></p>
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