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SSS Triangle Congruence Exploration by Jessica

SSS Triangle Congruence Exploration by Jessica
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2014-11-19 09:37
TriangleAngleTransformationGeometric Construction
In collections Triangle Congruence
① This example dynamically constructs triangles with fixed side lengths to visually demonstrate the Side-Side-Side (SSS) criterion for triangle congruence. ② The core mathematical concept is the SSS congruence rule, stating that if three sides of one triangle are equal to the corresponding sides of another, the triangles are congruent. It also involves basic triangle elements (sides, angles) and geometric transformations like translation or rotation. ③ Construction highlights: using GeoGebra commands Point, Segment, and Angle, multiple triangles and their corresponding sides (e.g., AB, BC, CA) are built, with auxiliary points (A_2, B_2, etc.) and lines (a, b, c, etc.) to compare different triangles, plus text labels (text1) and angle marks (α, β, γ) for observation. ④ Suitable for middle school geometry lessons, exploring triangle congruence conditions, and dynamic geometry experiments.

GeoGebra Commands & Parameters

  1. Point(Circle[B_2, abs(AB)]) → A_2
  2. Segment(B_2, A_2) → a
  3. Point(Circle[B_2, abs(BC)]) → C_2
  4. Segment(B_2, C_2) → b
  5. Point(Circle[C_2, abs(CA)]) → A_2'
  6. Segment(C_2, A_2') → c
  7. Point(Circle[B_1, abs(AB)]) → A_1
  8. Segment(B_1, A_1) → a_1
  9. Point(Circle[B_1, abs(BC)]) → C_1
  10. Segment(B_1, C_1) → b_1
  11. Point(Circle[C_1, abs(CA)]) → A_1'
  12. Segment(C_1, A_1') → c_1
  13. Angle(C_1, B_1, A_1') → α
  14. Angle(A_1', C_1, B_1) → β
  15. Angle(B_1, A_1', C_1) → γ
  16. Angle(C_2, B_2, A_2) → δ
  17. Angle(B_2, C_2, A_2') → ε
  18. Angle(C_2, A_2', B_2) → ζ

AI Drawing Prompt Reference

Draw two congruent triangles with sides AB, BC, and CA. First, draw a circle with center B and radius AB, and find point A_2 on the circle. Connect B and A_2 to form side a. Then, draw a circle with center B and radius BC, and find point C_2 on the circle. Connect B and C_2 to form side b. Next, draw a circle with center C_2 and radius CA, and find point A_2' on the circle. Connect C_2 and A_2' to form side c. Repeat the above steps with center B_1, radius AB, to find point A_1, and connect B_1 and A_1 to form side a_1. Then, draw a circle with center B_1 and radius BC, and find point C_1 on the circle. Connect B_1 and C_1 to form side b_1. Finally, draw a circle with center C_1 and radius CA, and find point A_1' on the circle. Connect C_1 and A_1' to form side c_1. Label each triangle's angles as α, β, γ and δ, ε, ζ.
The prompt above was compiled from the original drawing commands and is for reference only.