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Congruent Triangles Practice 2

Congruent Triangles Practice 2
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2018-06-26 04:36
TrianglePolygonAngleTransformationGeometric Construction
This interactive geometry exercise focuses on naming congruent triangles and justifying the congruence with appropriate reasons. Students can drag, rotate, and reflect the two triangles to visually compare corresponding sides and angles, then determine whether the triangles are congruent and select the correct congruence criterion (e.g., SSS, SAS, ASA). The core mathematical concepts include the definition of congruent triangles, correspondence of vertices, sides, and angles, and the standard congruence theorems. The construction uses GeoGebra commands such as Polygon, Vector, Angle, Intersect, Textfield, Segment, Midpoint, and Rotate, creating multiple triangle objects (poly1, poly1_1) with their associated sides, angles, vertices, and interactive text fields for answers. This resource is suitable for middle school geometry students learning triangle congruence, and can be used for classroom demonstrations or self-paced practice, enhancing conceptual understanding through dynamic manipulation.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Vector(P, A) → u
  3. Vector(P, B) → v
  4. Vector(P, C) → w
  5. Polygon(A_1, B_1, C_1) → poly1_1, c_1, a_1, b_1
  6. Vector(P_1, A_1) → u_1
  7. Vector(P_1, B_1) → v_1
  8. Vector(P_1, C_1) → w_1
  9. Angle(B, A, C) → α
  10. Angle(A, C, B) → β
  11. Angle(A_1, C_1, B_1) → γ
  12. Angle(B_1, A_1, C_1) → δ
  13. Intersect(Circle[X_0, Side_b], Circle[Y_0, Side_a]) → Z_0, L, ,
  14. Polygon(X_0, Y_0, Z_0) → poly2, z_0, x_0, y_0
  15. Textfield(text13) → Ans1
  16. Textfield(text14) → Ans2
  17. Segment(D, E) → r
  18. Midpoint(Segment[Intersect[Circle[A, r], b], Intersect[Circle[A, r], c]]) → F
  19. Midpoint(Segment[Intersect[Circle[C, r], a], Intersect[Circle[C, r], b]]) → G
  20. Midpoint(Segment[Intersect[Circle[A_1, r], b_1], Intersect[Circle[A_1, r], c_1]]) → H
  21. Midpoint(Segment[Intersect[Circle[C_1, r], a_1], Intersect[Circle[C_1, r], b_1]]) → I
  22. Angle(A_1, B_1, C_1) → ε
  23. Angle(C, B, A) → ζ
  24. Midpoint(Segment[Intersect[Circle[B, r], a], Intersect[Circle[B, r], c]]) → J
  25. Midpoint(Segment[Intersect[Circle[B_1, r], a_1], Intersect[Circle[B_1, r], c_1]]) → K
  26. Rotate(Translate[Mirror[X_0, x = 0], translate], (-(180° - Angle[Y_0, X_0, Z_0])), (11, 0)) → X_1
  27. Rotate(Translate[Mirror[Y_0, x = 0], translate], (-(180° - Angle[Y_0, X_0, Z_0])), (11, 0)) → Y_1
  28. Rotate(Translate[Mirror[Z_0, x = 0], translate], (-(180° - Angle[Y_0, X_0, Z_0])), (11, 0)) → Z_1