Question

are these figures congruent? hint: use rigid transformations. yes no

Explanation:

Step1: Recall congruent - figure definition

Two figures are congruent if one can be mapped onto the other by rigid transformations (translations, rotations, reflections).

Step2: Analyze the given triangles

The top - triangle has vertices at (-4, 1), (-3, 4), (-2, 1). The bottom - triangle has vertices at (-4, - 1), (-3, - 4), (-2, - 1). We can reflect the top - triangle over the x - axis. The rule for reflecting a point (x, y) over the x - axis is (x, -y). After reflection, the vertices of the top - triangle (-4, 1), (-3, 4), (-2, 1) become (-4, - 1), (-3, - 4), (-2, - 1) which are the same as the vertices of the bottom - triangle.

Answer:

Yes