Question

Congruent Polygons Write a congruence statement for the polygons explain in words a rigid motion that would map one triangle onto the other

Answer 1

For triangles ABC and MNL, since sides, AB and MN are equal and angles A and M are equal, we can use the theorem Side Angle Side (SAS) for congruency. The rigid motions that convert one triangle into the other are the following:

We translate the triangle ABC until point C and point L coincide then we rotate triangle ABC centered at C anticlockwise until both triangles coincide.

For triangles XYZ and VWU we can use the fact that all of their sides are equal, therefore we can use Side Side Side (SSS) theorem for congruency. The rigid motions are the following:

First, we translate triangle XYZ until points X and V coincide, then we reflect the triangle XYZ over its middle axis, and then we rotate anticlockwise triangle XYZ centered at X until both triangles coincide