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Exploring SSA for Triangle Congruence by Ted Coe

Exploring SSA for Triangle Congruence by Ted Coe
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2014-07-04 23:09
TriangleAngleGeometric Construction
In collections Congruence (CO) Cluster Congruence (Vol 1) Congruence (Vol 1) Over 80 Resources CCSS High School: Geometry (Congruence) Volume 1 S N ATTAR Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1
This example demonstrates why SSA (two sides and the included angle) does not establish triangle congruence. It involves the core mathematical concept of triangle congruence conditions. Using GeoGebra commands such as Circle, Ray, Intersect, Angle, Segment, etc., different scenarios of triangle constructions are illustrated. Suitable for high school geometry learners and educators.

GeoGebra Commands & Parameters

  1. Circle(A, b) → e
  2. Ray(A, C) → d
  3. Intersect(e, d) → K,
  4. Ray(A, B) → c
  5. Angle(B, A, C) → β
  6. Segment(A, D) → f
  7. Intersect(d, f) → E
  8. Intersect(d, f) → F
  9. Circle(D, a) → g
  10. Intersect(g, c) → G, H
  11. Segment(D, G) → h
  12. Segment(D, H) → i
  13. OrthogonalLine(D, c) → j
  14. Intersect(g, j, 1) → I
  15. Intersect(j, c) → J
  16. Distance(D, J) → k
  17. Segment(D, I) → l
  18. Distance(D, I) → m
  19. Distance(D, I) → Distance[D, J]
  20. Polygon(A, G, D) → poly1, d_1, a_1, g_1
  21. Polygon(A, H, D) → poly2, d_2, a_2, h_1
  22. Angle(D, G, A) → γ
  23. Angle(D, H, A) → δ

AI Drawing Prompt Reference

Draw two triangles sharing the base AD, with angles γ and δ at vertices A and D respectively. Start by drawing the base AD, then draw two circles with center D and different radii, intersecting the lines forming angles γ and δ at A and D, respectively, to create two triangles. Pay attention to whether these triangles are congruent to understand the implications of the SSA condition in triangle construction.
The prompt above was compiled from the original drawing commands and is for reference only.