MathPlotAI Logo MathPlotAI

SAS Congruence Theorem Demo

SAS Congruence Theorem Demo
Loading the math board and drawing, please wait…
2015-10-07 22:46
TriangleAngleGeometric Construction
In collections Triangle Congruence Theorems
This example demonstrates how to construct congruent triangles given two sides and the included angle (SAS), proving that non-congruent triangles cannot be formed under this condition. It involves core math concepts like congruence theorems, SAS relationships, and geometric constructions. The construction uses commands/objects such as Point, Segment, Rotate, Angle, Vector, and Translate from GeoGebra. Suitable for high school students learning the SAS congruence theorem and geometric constructions.

GeoGebra Commands & Parameters

  1. Point(Circle[B, a]) → C
  2. Segment(B, C) → b
  3. Rotate(C, α_1, B) → C'
  4. Angle(C, B, C') → α
  5. Point(Circle[B, d]) → D_1
  6. Segment(B, D_1) → e
  7. Rotate(D_1, α_1, B) → D
  8. Segment(B, D) → c
  9. Segment(D, C) → f
  10. Vector(A, E) → u
  11. Translate(B, u) → B'
  12. Translate(C, u) → C'_1
  13. Segment(B', C'_1) → b'
  14. Translate(B, u) → B'_1
  15. Translate(D, u) → D'
  16. Segment(B'_1, D') → c'
  17. Angle(C'_1, B', D') → β
  18. Segment(D', C'_1) → g