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SAS Congruence by GeoGebra Materials Team

SAS Congruence by GeoGebra Materials Team
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2012-05-03 19:12
TriangleAngleGeometric ConstructionSlider Animation
In collections Triangle Congruence - Collection
This interactive sheet demonstrates how the Side-Angle-Side (SAS) condition is sufficient for proving two triangles are congruent. It involves core math concepts like triangle congruence theorems, geometric constructions, and the relationships between angles and sides. The construction uses commands like Segment, Angle, Circle, Point, Rotate, Ray, and Intersect. Ideal for middle school students to visually grasp the application of the SAS congruence theorem.

GeoGebra Commands & Parameters

  1. Segment(A, B) → c
  2. Segment(B, C) → a
  3. Segment(C, A) → b
  4. Angle(A, C, B) → α
  5. Circle(D, b) → d
  6. Point(d) → E
  7. Segment(E, D) → e
  8. Rotate(E, α, D) → E'
  9. Angle(E, D, E') → β
  10. Ray(D, E') → f
  11. Circle(D, a) → g
  12. Intersect(g, f, 1.0) → F
  13. Segment(D, F) → h

AI Drawing Prompt Reference

Draw two triangles ABC and DEF, with AB equal to DE, angle BAC equal to angle EDF, and AC equal to EF. First, draw line segment AB, then draw angle BAC, next draw a circle with center A and radius AC, then pick point E on the circle, rotate point E to get point E' such that angle DE'E equals angle BAC, then draw ray DE', next draw a circle with center D and radius DE, finally find the intersection F of the two circles, and draw line segment DF.
The prompt above was compiled from the original drawing commands and is for reference only.