Constructing an Isometry

Below, you will construct an isometry that will map ΔABC to ΔA'B'C' by following these steps.

1. Do the triangles have the same orientation?
If YES go to #2.
If NO, go to #3 AFTER the mathlet.
2. The two triangles must be related by a rotation. Rotate ΔABC using the GREEN α slider for the rotation angle and the GREEN CENTER point as the center of rotation. Move the CENTER point and adjust the angle until ΔABC coincides with ΔA'B'C'.

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3. Translate ΔABC using the PURPLE TRANSLATE vector so that any one of A, B, or C coincides with A', B', or C', respectively.
4. The translated triangle and ΔA'B'C' either coincide or are now related by a reflection. Use the RED REFLECT line to reflect your translated triangle. Move the REFLECT line until your images coincide.

What does this activity say about constructing isometries?

Steve Phelps, Created with GeoGebra