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三角形内角和计算示例

三角形内角和计算示例
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2015-11-11 05:07
测试改名0角几何作图
所属专题 CCSS Support Math I Unit 5
①本范例演示了如何通过 GeoGebra 计算三角形的未知内角；②涉及的核心数学概念为三角形内角和定理；③作图要点：使用 LaTeX 命令显示文本，CircleSector 绘制角度扇形，SelectedElement 和 SelectedIndex 实现交互选择，对象包括 text2, text6, text12 等；④适合初中数学教学，用于理解和应用三角形内角和定理。

GeoGebra 命令及参数

  1. LaTeX("\text{Determine the total measure of the two known angles.}") → text2
  2. LaTeX("\text{Use the result to determine the measure of the third angle.}") → text6
  3. LaTeX("\text{The sum of the measures is \textcolor{#000099}{180°}.}") → text12
  4. CircleSector(C_1, D_1, E_1) → c
  5. CircleSector(C_1, G_1, H_1) → d
  6. SelectedElement(A) → a1
  7. SelectedElement(B) → b1
  8. SelectedIndex(A) → A1
  9. SelectedIndex(B) → B1
  10. LaTeX((((("\text{A triangle has two angles that measure \textcolor{#000099}{" * a1) * "} and \textcolor{#000099}{") * b1) * "}. What is the measure of the third angle?}")) → text1
  11. LaTeX((((("\text{The two known angle measures of the triangle are \textcolor{#000099}{" * a1) * "} and \textcolor{#000099}{") * b1) * "}. To find the total, add the known measures.}")) → text3
  12. LaTeX((((((("\text{\textcolor{#000099}{" * a1) * " + ") * b1) * " = ") * ab) * "}}")) → text4
  13. LaTeX((("\text{Subtract \textcolor{#000099}{" * ab) * "} from both sides of the equation.}")) → text14
  14. LaTeX((("\text{ \textcolor{#000099}{" * ab) * " + x = 180°}}")) → text11
  15. LaTeX((("\text{ \textcolor{#000099}{x =" * sol) * "}}")) → text13
  16. LaTeX("\text{Let \textcolor{#000099}{x} represent the unknown measure of the third angle.}") → text8
  17. LaTeX("\text{\mathbf{Congruent\; angles} two angles that have the same measure.}") → text17
  18. LaTeX("\text{A}") → text19
  19. LaTeX("\text{B}") → text19_1
  20. LaTeX("\text{then solve for \textcolor{#000099}{x}.}") → text10
  21. LaTeX("\text{\mathbf{Congruent\;triangles} triangles having the same angle measures and side lengths.}") → text17_4
  22. LaTeX("\text{Select the angles: }") → text18
  23. LaTeX((("\text{The total measure of the two known angles is \textcolor{#000099}{" * ab) * "}.}")) → text5
  24. LaTeX("\text{The sum of the measures of the angles is \textcolor{#000099}{180°}. Write and solve an equation to find the third angle.}") → text7
  25. LaTeX((("\text{The third angle measures \textcolor{#000099}{" * sol) * "}.}")) → text15
  26. LaTeX((("\text{There are different ways to set up the equation. For example, we can add \textcolor{#000099}{" * ab) * "} and \textcolor{#000099}{x} and set them equal to \textcolor{#000099}{180°},}")) → text9