Bài 4: Đường Trung Bình Của Tam Giác - Hình Thang
Hướng dẫn giải Bài 26 (Trang 80 SGK Toán Hình học 8, Tập 1)
<p><strong class="content_question">Đề bài</strong></p>
<p>Tính <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>x</mi><mo>,</mo><mi>y</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">x</span></span><span id="MJXc-Node-4" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-5" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">y</span></span></span></span></span> trên hình <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"><mn>45</mn></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-mn"><span class="mjx-char MJXc-TeX-main-R">45</span></span></span></span></span>, trong đó <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>B</mi><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>C</mi><mi>D</mi><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>E</mi><mi>F</mi><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>G</mi><mi>H</mi><mo>.</mo></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 id="MJXc-Node-12" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-13" class="mjx-texatom"><span id="MJXc-Node-14" class="mjx-mrow"><span id="MJXc-Node-15" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-16" class="mjx-texatom"><span id="MJXc-Node-17" class="mjx-mrow"><span id="MJXc-Node-18" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-19" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-20" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span><span id="MJXc-Node-21" class="mjx-texatom"><span id="MJXc-Node-22" class="mjx-mrow"><span id="MJXc-Node-23" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-24" class="mjx-texatom"><span id="MJXc-Node-25" class="mjx-mrow"><span id="MJXc-Node-26" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-27" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-28" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span><span id="MJXc-Node-29" class="mjx-texatom"><span id="MJXc-Node-30" class="mjx-mrow"><span id="MJXc-Node-31" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-32" class="mjx-texatom"><span id="MJXc-Node-33" class="mjx-mrow"><span id="MJXc-Node-34" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-35" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">G</span></span><span id="MJXc-Node-36" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">H</span></span><span id="MJXc-Node-37" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">.</span></span></span></span></span></p>
<p><span 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><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>C</mi><mi>D</mi><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>E</mi><mi>F</mi><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>G</mi><mi>H</mi><mo>.</mo></math>"><span class="mjx-math" aria-hidden="true"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"><img class="wscnph" style="max-width: 100%;" src="https://static.colearn.vn:8413/v1.0/upload/library/30062022/01c53120-c729-46e0-af24-fe82822a3885.PNG" /></span></span></span></span></span></p>
<p><strong class="content_detail">Lời giải chi tiết</strong></p>
<p>- Vì <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><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>E</mi><mi>F</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">B</span></span><span id="MJXc-Node-42" class="mjx-texatom"><span id="MJXc-Node-43" class="mjx-mrow"><span id="MJXc-Node-44" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-45" class="mjx-texatom"><span id="MJXc-Node-46" class="mjx-mrow"><span id="MJXc-Node-47" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">/</span></span></span></span><span id="MJXc-Node-48" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span><span id="MJXc-Node-49" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span></span></span></span> nên <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><mi>F</mi><mi>E</mi></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-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-53" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-54" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span><span id="MJXc-Node-55" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span></span></span></span> là hình thang (dấu hiệu nhận biết hình thang)</p>
<p>Vì <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>C</mi><mi>A</mi><mo>=</mo><mi>C</mi><mi>E</mi></math>"><span id="MJXc-Node-56" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-57" class="mjx-mrow"><span id="MJXc-Node-58" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><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-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-61" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-62" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span></span></span></span> (giả thiết) và <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><mi>B</mi><mo>=</mo><mi>D</mi><mi>F</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">D</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-mo MJXc-space3"><span class="mjx-char MJXc-TeX-main-R">=</span></span><span id="MJXc-Node-68" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">D</span></span><span id="MJXc-Node-69" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span></span></span></span> (giả thiết) </p>
<p> <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"><mo stretchy="false">&#x21D2;</mo><mi>C</mi><mi>D</mi></math>"><span id="MJXc-Node-70" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-71" class="mjx-mrow"><span id="MJXc-Node-72" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">⇒</span></span><span id="MJXc-Node-73" class="mjx-mi MJXc-space3"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-74" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span></span></span></span> là đường trung bình của hình thang <span id="MathJax-Element-9-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>B</mi><mi>F</mi><mi>E</mi></math>"><span id="MJXc-Node-75" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-76" class="mjx-mrow"><span id="MJXc-Node-77" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-78" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-79" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">F</span></span><span id="MJXc-Node-80" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">E</span></span></span></span></span> (dấu hiệu nhận biết đường trung bình của hình thang)</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>⇒</mo><mi>C</mi><mo>⁢</mo><mi>D</mi><mo>=</mo><mfrac><mrow><mi>A</mi><mo>⁢</mo><mi>B</mi><mo>+</mo><mi>E</mi><mo>⁢</mo><mi>F</mi></mrow><mn>2</mn></mfrac><mo>=</mo><mfrac><mrow><mn>8</mn><mo>+</mo><mn>16</mn></mrow><mn>2</mn></mfrac><mo>=</mo><mpadded><mn>12</mn></mpadded><mo>⁢</mo><mi>cm</mi></mstyle></math> (tính chất đường trung bình của hình thang)<br />Hay <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mpadded><mn>12</mn></mpadded><mo>⁢</mo><mi>cm</mi><mo>.</mo></math><br />- vi CD//HG nên CDHG là hình thang (dấu hiệu nhận biết hình thang)<br />vì GE=CE (giả thiết) và FH=DF (giả thiết)<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>⇒</mo><mi>E</mi><mo>⁢</mo><mi>F</mi></mstyle></math> là đường trung bình của hình thang CDHG (dấu hiệu nhận biết đường trung bình của hình thang)<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mstyle displaystyle="false"><mo>⇒</mo><mi>E</mi><mo>⁢</mo><mi>F</mi><mo>=</mo><mfrac><mrow><mi>C</mi><mo>⁢</mo><mi>D</mi><mo>+</mo><mi>G</mi><mo>⁢</mo><mi>H</mi></mrow><mn>2</mn></mfrac></mstyle></math> (tính chất đường trung bình của hình thang)<br /><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>G</mi><mo>⁢</mo><mi>H</mi><mo>=</mo><mn>2</mn><mo>⁢</mo><mi>E</mi><mo>⁢</mo><mi>F</mi><mo>-</mo><mi>C</mi><mo>⁢</mo><mi>D</mi><mo>=</mo><mn>2.16</mn><mo>-</mo><mn>12</mn></math></p>
<p>GH=20cm hay y=20cm}.<br />Vậy x=12cm, y=20cm.</p>
<p><span 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><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>C</mi><mi>D</mi><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>E</mi><mi>F</mi><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mi>G</mi><mi>H</mi><mo>.</mo></math>"><span class="mjx-math" aria-hidden="true"><span class="mjx-mrow"><span class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R"><br /><br /><br /></span></span></span></span></span></p>
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