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SSS to Prove Triangles Congruent

SSS to Prove Triangles Congruent
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2019-02-06 08:21
TrianglePolygonAngleGeometric Construction
In collections Triangle Congruence Criteria Visual Representations
This example demonstrates how to use the SSS (Side-Side-Side) criterion to prove that two triangles are congruent. Key mathematical concepts include the SSS congruence theorem. Using GeoGebra commands such as Circle, Segment, Point, Intersect, Polygon, and Angle, you can construct two congruent triangles. Suitable for middle school and above students to learn geometric construction and triangle congruence criteria.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Circle(C, B) → d
  3. Segment(C, A) → a
  4. Segment(C, B) → b
  5. Segment(B, A) → e
  6. Point(Circle[D, abs(a)]) → E
  7. Segment(D, E) → f
  8. Circle(D, b) → g
  9. Circle(E, e) → h
  10. Intersect(g, h, 1) → F
  11. Segment(F, D) → i
  12. Segment(F, E) → j
  13. Polygon(C, B, A) → poly1, a_1, c_1, b_1
  14. Polygon(D, F, E) → poly2, e_1, d_1, f_1
  15. Angle(C, B, A) → α
  16. Angle(B, A, C) → β
  17. Angle(A, C, B) → γ
  18. Angle(D, F, E) → δ
  19. Angle(F, E, D) → ε
  20. Angle(E, D, F) → ζ

AI Drawing Prompt Reference

Draw two triangles to demonstrate congruence by SSS. Start with a segment as a common side. Using its endpoints as centers, draw two arcs with radii equal to the other two side lengths; their intersection gives the third vertex, forming the first triangle. Then copy the base segment for the second triangle. From one endpoint, draw an arc with radius equal to the second side of the first triangle; from the other endpoint, draw an arc with radius equal to the third side. Their intersection gives the new third vertex; connect to form the second triangle. Finally, label all interior angles of both triangles and show that corresponding angles are equal.
The prompt above was compiled from the original drawing commands and is for reference only.