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.
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'