Question

K12 help??? 3.12 Congruence and Rigid Motions

Answer 1

Congruent because you can map the triangles using a reflection across the y-axis which is a rigid motion

Answer 2

Answer: ΔPQR is congruent to ΔP'Q'R'  because We can map ΔPQR to ΔP'Q'R' using reflection across y-axis. which is a rigid motion.

Step-by-step explanation:

Given : The coordinates of ΔPQR are P(1,4) , Q(2,2)  and R(-2, 1).

The coordinates of  ΔP'Q'R' are P(-1,4) , Q(-2,2)  and R(2, 1).

Note that the sign of x-coordinate is changed but the magnitude of x and y coordinates remains unchanged.

It means we can ΔP'Q'R' is a mirror image of ΔPQR across y-axis (∵ y-values are exactly same.)

i.e. We can map ΔPQR to ΔP'Q'R' using reflection across y-axis.

Since reflection is a rigid motion and all rigid motions produces congruent images.

⇒ ΔPQR is congruent to  ΔP'Q'R'