Similar Triangles - Reflection in a Mirror

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2015-12-02 08:58

Angle Geometric Construction

This example demonstrates the geometric phenomenon of similar triangles under mirror reflection. Core math concepts involved include angles, geometry, reflection, similar triangles, and similarity transformation. Construction highlights the use of GeoGebra commands: Segment, Midpoint, Line, Point, OrthogonalLine, Mirror, Ray, Intersect, Angle; and objects like A, B, Mirror, C, a, D, E, b, c, Eyes, d, e, F', C', d', f, Eye, FRIEND, YOU, α, β, i, j, k, text1. Suitable for middle school students learning geometry and similarity transformations.

GeoGebra Commands & Parameters

Segment(A, B) → Mirror
Midpoint(Mirror) → C
Line(A, B) → a
Point(a) → D
Point(a) → E
OrthogonalLine(D, a) → b
OrthogonalLine(E, a) → c
Point(b) → Eyes
Segment(Eyes, C) → d
OrthogonalLine(C, Mirror) → e
Mirror(Eyes, e) → F'
Mirror(C, e) → C'
Segment(F', C') → d'
Ray(C, F') → f
Intersect(f, c) → Eye
Segment(Eye, E) → FRIEND
Segment(Eyes, D) → YOU
Angle(B, C, Eye) → α
Angle(Eyes, C, A) → β
Segment(C, D) → i
Segment(C, E) → j
Segment(C, Eye) → k