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Congruent Triangles: Angle-Side-Angle

Congruent Triangles: Angle-Side-Angle
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2012-05-03 19:11
TriangleAngleGeometric Construction
In collections Triangle Congruence - Collection
This interactive sheet demonstrates the congruence of triangles under the Angle-Side-Angle (ASA) condition. It involves the core mathematical concept of triangle congruence. Using GeoGebra commands such as Segment, Circle, Angle, etc., two triangles satisfying the ASA condition are constructed and their congruence is observed. Suitable for students at the junior high school level and above to learn about triangle congruence.

GeoGebra Commands & Parameters

  1. Segment(A, B) → c
  2. Segment(B, C) → a
  3. Segment(C, A) → b
  4. Circle(D, c) → d
  5. Point(d) → E
  6. Segment(D, E) → e
  7. Angle(B, A, C) → α
  8. Angle(C, B, A) → β
  9. Rotate(E, α, D) → E'
  10. Angle(E, D, E') → γ
  11. Ray(D, E') → f
  12. Rotate(D, -(β), E) → D'
  13. Angle(D', E, D) → δ
  14. Ray(E, D') → g
  15. Point(f) → F
  16. Point(g) → G
  17. Segment(D, F) → h
  18. Segment(E, G) → i

AI Drawing Prompt Reference

Draw two congruent triangles to demonstrate the Angle-Side-Angle (ASA) congruence condition. Start by constructing a triangle with two angles and the included side labeled. Then, draw a circle centered at one angle with the included side as the radius, connecting the intersection point to the vertex. Rotate the newly formed angle to create a second triangle, ensuring both satisfy the ASA condition and display their congruence.
The prompt above was compiled from the original drawing commands and is for reference only.