ASA Congruence: Constructing Congruent Triangles via Rotation and Intersection
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① This example demonstrates how to construct two congruent triangles using the ASA (Angle-Side-Angle) criterion, visually confirming the congruence theorem. ② Core mathematical concepts include triangle congruence (ASA), angle measurement, segment length, rotation, and intersection of lines. ③ Construction steps: Using GeoGebra commands Point, Segment, Rotate, Angle, Line, and Intersect, points A, B, C and rotated points A', B' are created; angles α, β, γ and segments define the sides; lines and intersections determine vertices D, E, F, yielding two congruent triangles. ④ Suitable for middle school geometry lessons to illustrate congruence conditions, and as a dynamic tool for exploring corresponding parts under rotation.
GeoGebra Commands & Parameters
Point(Circle[A, b]) → BSegment(A, B) → fRotate(B, α, A) → B'Angle(B, A, B') → γLine(A, B') → gRotate(A, (-β), B) → A'Angle(A', B, A) → δLine(B, A') → hIntersect(h, g) → CSegment(A, C) → iSegment(C, B) → jPoint(Circle[D, b]) → ESegment(D, E) → kRotate(E, α, D) → E'Angle(E, D, E') → εLine(D, E') → lRotate(D, (-β), E) → D'Angle(D', E, D) → ζLine(E, D') → mIntersect(m, l) → FSegment(D, F) → nSegment(F, E) → pAngle(A, C, B) → ηAngle(D, F, E) → θSegment(A, B) → q