Bài 1: Tứ Giác
Hướng dẫn giải Bài 5 (Trang 67 SGK Toán Hình học 8, Tập 1)
<p><strong class="content_question">Đề bài</strong></p>
<p>Đố em tìm thấy vị trí của "kho báu" trên hình <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"><mn>11</mn></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-mn"><span class="mjx-char MJXc-TeX-main-R">11</span></span></span></span></span>, biết rằng kho báu nằm tại giao điểm các đường chéo của tứ giác <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>B</mi><mi>C</mi><mi>D</mi></math>"><span id="MJXc-Node-4" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-5" class="mjx-mrow"><span id="MJXc-Node-6" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-7" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-8" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-9" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span></span></span></span>, trong đó các đỉnh của tứ giác có tọa độ như sau: <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><mo stretchy="false">(</mo><mn>3</mn><mo>;</mo><mn>2</mn><mo stretchy="false">)</mo><mo>,</mo><mi>B</mi><mo stretchy="false">(</mo><mn>2</mn><mo>;</mo><mn>7</mn><mo stretchy="false">)</mo><mo>,</mo><mi>C</mi><mo stretchy="false">(</mo><mn>6</mn><mo>;</mo><mn>8</mn><mo stretchy="false">)</mo><mo>,</mo><mi>D</mi><mo stretchy="false">(</mo><mn>8</mn><mo>;</mo><mn>5</mn><mo stretchy="false">)</mo><mo>.</mo></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">A</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-mn"><span class="mjx-char MJXc-TeX-main-R">3</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-mn MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">2</span></span><span id="MJXc-Node-17" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">)</span></span><span id="MJXc-Node-18" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-19" class="mjx-mi MJXc-space1"><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-mn"><span class="mjx-char MJXc-TeX-main-R">2</span></span><span id="MJXc-Node-22" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">;</span></span><span id="MJXc-Node-23" class="mjx-mn MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">7</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-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-26" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-27" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">(</span></span><span id="MJXc-Node-28" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">6</span></span><span id="MJXc-Node-29" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">;</span></span><span id="MJXc-Node-30" class="mjx-mn MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">8</span></span><span id="MJXc-Node-31" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">)</span></span><span id="MJXc-Node-32" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-33" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">D</span></span><span id="MJXc-Node-34" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">(</span></span><span id="MJXc-Node-35" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">8</span></span><span id="MJXc-Node-36" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">;</span></span><span id="MJXc-Node-37" class="mjx-mn MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">5</span></span><span id="MJXc-Node-38" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">)</span></span><span id="MJXc-Node-39" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">.</span></span></span></span></span></p>
<p><strong class="content_detail">Lời giải chi tiết</strong></p>
<p>Các bước làm như sau: </p>
<p>- Xác định các điểm <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><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>,</mo><mi>D</mi></math>"><span id="MJXc-Node-46" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-47" class="mjx-mrow"><span id="MJXc-Node-48" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-49" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-50" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-51" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-52" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-53" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-54" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">D</span></span></span></span></span> trên hình vẽ 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>A</mi><mo stretchy="false">(</mo><mn>3</mn><mo>;</mo><mn>2</mn><mo stretchy="false">)</mo><mo>,</mo><mi>B</mi><mo stretchy="false">(</mo><mn>2</mn><mo>;</mo><mn>7</mn><mo stretchy="false">)</mo><mo>,</mo><mi>C</mi><mo stretchy="false">(</mo><mn>6</mn><mo>;</mo><mn>8</mn><mo stretchy="false">)</mo><mo>,</mo><mi>D</mi><mo stretchy="false">(</mo><mn>8</mn><mo>;</mo><mn>5</mn><mo stretchy="false">)</mo></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">A</span></span><span id="MJXc-Node-58" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">(</span></span><span id="MJXc-Node-59" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">3</span></span><span id="MJXc-Node-60" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">;</span></span><span id="MJXc-Node-61" class="mjx-mn MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">2</span></span><span id="MJXc-Node-62" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">)</span></span><span id="MJXc-Node-63" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-64" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-65" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">(</span></span><span id="MJXc-Node-66" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">2</span></span><span id="MJXc-Node-67" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">;</span></span><span id="MJXc-Node-68" class="mjx-mn MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">7</span></span><span id="MJXc-Node-69" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">)</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 id="MJXc-Node-72" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">(</span></span><span id="MJXc-Node-73" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">6</span></span><span id="MJXc-Node-74" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">;</span></span><span id="MJXc-Node-75" class="mjx-mn MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">8</span></span><span id="MJXc-Node-76" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">)</span></span><span id="MJXc-Node-77" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">,</span></span><span id="MJXc-Node-78" class="mjx-mi MJXc-space1"><span class="mjx-char MJXc-TeX-math-I">D</span></span><span id="MJXc-Node-79" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">(</span></span><span id="MJXc-Node-80" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">8</span></span><span id="MJXc-Node-81" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">;</span></span><span id="MJXc-Node-82" class="mjx-mn MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">5</span></span><span id="MJXc-Node-83" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">)</span></span></span></span></span>.</p>
<p>- Vẽ tứ giác <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>A</mi><mi>B</mi><mi>C</mi><mi>D</mi><mo>.</mo></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">A</span></span><span id="MJXc-Node-87" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">B</span></span><span id="MJXc-Node-88" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span><span id="MJXc-Node-89" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">D</span></span><span id="MJXc-Node-90" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">.</span></span></span></span></span></p>
<p>- Vẽ hai đường chéo <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>A</mi><mi>C</mi></math>"><span id="MJXc-Node-91" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-92" class="mjx-mrow"><span id="MJXc-Node-93" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">A</span></span><span id="MJXc-Node-94" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">C</span></span></span></span></span> và <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>B</mi><mi>D</mi></math>"><span class="MJX_Assistive_MathML" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mi>D</mi></math></span></span>. Gọi <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>K</mi></math>"><span id="MJXc-Node-99" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-100" class="mjx-mrow"><span id="MJXc-Node-101" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">K</span></span></span></span></span> là giao điểm của hai đường chéo đó.</p>
<p>- Xác định tọa độ của 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>K</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">K</span></span></span></span></span> là <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><mo stretchy="false">(</mo><mn>5</mn><mo>;</mo><mn>6</mn><mo stretchy="false">)</mo></math>"><span id="MJXc-Node-105" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-106" class="mjx-mrow"><span id="MJXc-Node-107" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">K</span></span><span id="MJXc-Node-108" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">(</span></span><span id="MJXc-Node-109" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">5</span></span><span id="MJXc-Node-110" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">;</span></span><span id="MJXc-Node-111" class="mjx-mn MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">6</span></span><span id="MJXc-Node-112" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">)</span></span></span></span></span></p>
<p>Vậy vị trí kho báu có tọa độ <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>K</mi><mo stretchy="false">(</mo><mn>5</mn><mo>;</mo><mn>6</mn><mo stretchy="false">)</mo></math>"><span id="MJXc-Node-113" class="mjx-math" aria-hidden="true"><span id="MJXc-Node-114" class="mjx-mrow"><span id="MJXc-Node-115" class="mjx-mi"><span class="mjx-char MJXc-TeX-math-I">K</span></span><span id="MJXc-Node-116" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">(</span></span><span id="MJXc-Node-117" class="mjx-mn"><span class="mjx-char MJXc-TeX-main-R">5</span></span><span id="MJXc-Node-118" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">;</span></span><span id="MJXc-Node-119" class="mjx-mn MJXc-space1"><span class="mjx-char MJXc-TeX-main-R">6</span></span><span id="MJXc-Node-120" class="mjx-mo"><span class="mjx-char MJXc-TeX-main-R">)</span></span></span></span></span> trên hình vẽ. </p>
<p><img src="https://vietjack.com/giai-toan-lop-8/images/bai-5-trang-67-sgk-toan-8-tap-1-2.PNG" alt="Giải bài 5 trang 67 Toán 8 Tập 1 | Giải bài tập Toán 8" /></p>
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Hướng dẫn giải Câu hỏi 3 (Trang 65 SGK Toán Hình học 8, Tập 1)
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Hướng dẫn giải Bài 1 (Trang 66 SGK Toán Hình học 8, Tập 1)
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Hướng dẫn giải Bài 2 (Trang 66 SGK Toán Hình học 8, Tập 1)
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Hướng dẫn giải Bài 3 (Trang 67 SGK Toán Hình học 8, Tập 1)
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Hướng dẫn giải Bài 4 (Trang 67 SGK Toán Hình học 8, Tập 1)
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