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SSS Congruence via Construction

SSS Congruence via Construction
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2019-04-09 02:08
TriangleAngleGeometric Construction
In collections Triangle Congruence
This example demonstrates how to create an exact copy of a triangle using geometric constructions to prove triangle congruence. Key math concepts include triangle congruence criteria and geometric constructions. Construction highlights involve GeoGebra commands like Circle, Point, Rotate, Ray, Intersect, Segment, and Angle; suitable for middle school and above, focusing on geometric constructions and triangle congruence.

GeoGebra Commands & Parameters

  1. Circle(A, b) → p
  2. Circle(A, 0.8) → c
  3. Point(c) → B_1
  4. Rotate(B_1, 30°, A) → B'
  5. Ray(A, B') → i
  6. Ray(A, B_1) → l
  7. Intersect(p, l, 1) → C
  8. Circle(A, 2) → k
  9. Intersect(k, i, 1) → B
  10. Segment(C, B) → m
  11. Angle(B_1, A, B') → α
  12. Segment(A, B) → j
  13. Segment(A, C) → n
  14. Circle(D, Segment[A, B]) → d
  15. Point(d) → E
  16. Segment(D, E) → f

AI Drawing Prompt Reference

Draw a triangle ABC and use geometric constructions to create an exact copy A'B'C' of it. Start by drawing two circles with different radii centered at point A, select a point B1 on the smaller circle, rotate it 30 degrees around A to get B', then draw a ray from A through B'. The intersection of this ray with the larger circle is point B. Connect AB and AC, then draw a circle centered at A, and find point C where it intersects the ray. Connect BC. Finally, construct triangle A'B'C' such that A'B' is congruent to AB, B'C' to BC, and A'C' to AC.
The prompt above was compiled from the original drawing commands and is for reference only.