Constructing an Isometry 3

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 or a translation. Construct the perpendicular bisectors of the coorresponding vertices. These perpendicular bisectors should be concurrent. This is the center of rotation. Construct the rotation.

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3. The two triangles must be related by a reflection or glide reflection. Construct the midpoints of the corresponding vertices. These midpoints should be collinear. The line through the midpoints is your reflection line.
4. After this reflection, the two triangles either coincide, or require a translation to coincide.

Steve Phelps, Created with GeoGebra