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Congruence of Triangles: Problem 52, Page 74

Congruence of Triangles: Problem 52, Page 74
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2011-11-10 00:22
TriangleAngleGeometric Construction
In collections Similarity and Congruence Year 8 Pedagogies in Practice
This example demonstrates how to prove the congruence of two triangles. Key mathematical concepts include the criteria for triangle congruence. Using GeoGebra commands such as Segment (线段), Midpoint (中点), OrthogonalLine (垂线), Point (点), Ray (射线), Intersect (交点), Angle (角), etc., two congruent triangles can be constructed. Suitable for students at the junior high school level and above for learning geometric proofs.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Midpoint(A, B) → H
  3. OrthogonalLine(H, a) → b
  4. Point(b) → C
  5. Segment(A, C) → c
  6. Segment(B, C) → d
  7. Point(b) → P
  8. Ray(A, P) → e
  9. Intersect(e, d) → E
  10. Ray(B, P) → f
  11. Intersect(f, c) → F
  12. Segment(P, F) → g
  13. Segment(P, E) → h
  14. Segment(P, B) → i
  15. Segment(A, P) → j
  16. Angle(P, H, A) → α
  17. Segment(C, H) → k

AI Drawing Prompt Reference

Draw two congruent triangles to demonstrate how to prove their congruence. Start by drawing a line segment, finding its midpoint, and drawing a perpendicular line. Locate a point on the segment and connect the endpoints to this point. Then, from this point, draw rays to the perpendicular line and the other side, intersecting them with the other side and the line connecting the endpoints. Connect these intersection points to form two congruent triangles, and label one of the angles.
The prompt above was compiled from the original drawing commands and is for reference only.