Question

Use rigid motions to explain whether the triangles in the figure are congruent. Be sure to describe specific rigid motions in your explanation.

Answer 1

Rigid motion of a plane is a transformation where the original and new image are congruent. In short, it's also known as isometry.

In the case above, ΔDWP is presumed to be congruent to ΔMJS. Rigid motions involved here are translation and rotation.

In translation, you are basically sliding/moving the figure. ΔDWP is moved five (5) units down then one (1) unit to the left. Thereby, coinciding point W of ΔDWP and point J of ΔMJS.

Next rigid motion used is rotation. The figure is simply rotated approximately 90 degrees thereby coinciding all points of ΔDWP to ΔMJS.

To check for congruency by just merely looking on the plane, compare the lengths of the sides of the triangles.

side DW = side MJ = 2 units
side WP = side JS = 4 units
side PD = side SM = 5 units

Therefore, we can say that ΔDWP is congruent to ΔMJS.