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全等三角形对应边角关系

全等三角形对应边角关系
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2015-11-12 03:11
测试改名0几何作图滑块动画
所属专题 CCSS Support Math I Unit 5
①本范例演示了两个全等三角形ABC与EDF的对应边角关系；②涉及核心数学概念：全等三角形判定、对应边角关系；③作图要点：使用LaTeX命令、线段Segment、镜像Mirror等GeoGebra命令和对象；④适合初中及以上学生学习几何证明和空间想象能力。

GeoGebra 命令及参数

  1. LaTeX("\text{Determine the corresponding angles.}") → SubQuestion1
  2. LaTeX("\text{Congruent triangles are named so that corresponding parts are}") → step1_1
  3. LaTeX("\text{named in the same sequence.}") → step1_2
  4. LaTeX("\text{Determine the corresponding sides.}") → step4
  5. LaTeX("\text{are named in the same sequence.}") → step5_2
  6. LaTeX("\text{\mathbf{Corresponding \;angles} angles of two figures that lie in the same position relative to}") → words1_1
  7. LaTeX("\text{\mathbf{Corresponding \;sides} sides of two figures that lie in the same position relative}") → words2_1
  8. Segment(A, B) → a_1
  9. Segment(B, C) → b
  10. Segment(A, C) → c
  11. Segment(dummy1, dummy2) → dummy
  12. Mirror(Border, dummy) → Border'
  13. Mirror(A, dummy) → E
  14. Mirror(Border, dummy) → Border'_1
  15. Mirror(B, dummy) → D
  16. Mirror(C, dummy) → F
  17. Segment(F, D) → d
  18. Segment(D, E) → e
  19. Segment(F, E) → f
  20. LaTeX("\text{ the figure.In transformations,the corresponding vertices are the preimage and}") → words1_2
  21. LaTeX("\text{ to the figure.In transformations,the corresponding sides are the preimage and}") → words2_2
  22. LaTeX("\text{image sides,so \textcolor{#000099}{\(\overline{AB}\)} and \textcolor{#000099}{\(\overline{A'}\) \(\overline{B'}\)} are corresponding sides and so on.}") → words2_3
  23. LaTeX("\text{image vertices,so \textcolor{#000099}{∠A} and \textcolor{#000099}{∠A`} are corresponding vertices and so on. }") → words1_3
  24. LaTeX("\text{In the following diagram, \textcolor{#000099}{ \triangle ABC} is congruent to \textcolor{#000099}{\triangle EDF}. List all corresponding angles and sides.}") → Question
  25. LaTeX("\text{For this reason, in \textcolor{#000099}{\triangle ABC} and \textcolor{#000099}{\triangle{EDF}}, \textcolor{#000099}{\angle{A}} corresponds to \textcolor{#000099}{\angle{E},}}") → step2_1
  26. LaTeX("\text{\textcolor{#000099}{\angle B} corresponds to \textcolor{#000099}{\angle D}, and \textcolor{#000099}{\angle C} corresponds to \textcolor{#000099}{\angle F}.}") → step2_2
  27. LaTeX("\text{Again, congruent triangles are named so that corresponding parts}") → step5_1
  28. LaTeX("\text{For this reason, in \textcolor{#000099}{\triangle ABC} and \textcolor{#000099}{\triangle EDF}, \textcolor{#000099}{\(\overline{AB}\)} corresponds to \textcolor{#000099}{ \(\overline{ED}\)},}") → step6_1
  29. LaTeX("\text{\textcolor{#000099}{\(\overline{BC}\)} corresponds to \textcolor{#000099}{ \(\overline{DF}\)}, and \textcolor{#000099}{\(\overline{CA}\)} corresponds to \textcolor{#000099}{\(\overline{FE}\)}.}") → step6_2