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Corresponding Angles and Sides of Congruent Triangles

Corresponding Angles and Sides of Congruent Triangles
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2015-11-12 03:11
TriangleGeometric ConstructionSlider Animation
In collections CCSS Support Math I Unit 5
This example demonstrates the corresponding angles and sides of two congruent triangles, ABC and EDF. Key math concepts include triangle congruence criteria and relationships between corresponding parts. Construction involves commands like LaTeX, Segment, Mirror, and objects such as sliders and definitions in GeoGebra. Suitable for middle school and above students learning geometric proofs and spatial reasoning.

GeoGebra Commands & Parameters

  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