Because rigid motions preserve angle and length measurements, congruent figures have the same angles measures and side lengths. The quadrilaterals below are all congruent to each other.
Use rigid motion to determine if the two triangles are congruent.
If the triangles are congruent, that means that there exist one or several rigid motions that maps them onto each other. Let's see if we can find it. Both triangles are isosceles, so the equal sides must correspond to each other. Rotating the blue triangle clockwise around its center will orient it the same way as the red triangle.
Now, they have the same orientation. We can translate the blue triangle, by translating the vertex up units and to the right units.
Notice that, although one vertex has been mapped onto another, the other vertices do not align. This is because one pair of corresponding sides are not the same length. Thus, the triangles are not congruent.