Question

consider the figures graphed below. complete each congruence statement and describe a congruence transformation to make that maps each of the figures. a. defg ≅□_____, by□defg ... b. △abc ≅△___, by △abc ... c. △pqr ≅△_____, by △pqr ...

Explanation:

Step1: Identify congruent figures for part a

By observing the grid - based figures, rectangle $DEFG$ and rectangle $JKLM$ have the same shape and size. The transformation from $DEFG$ to $JKLM$ is a translation. We can count the number of units of horizontal and vertical movement.

Step2: Identify congruent figures for part b

Triangle $ABC$ and triangle $UTS$ have the same shape and size. The transformation from $\triangle ABC$ to $\triangle UTS$ is a reflection across the $y$ - axis.

Step3: Identify congruent figures for part c

Triangle $PQR$ and triangle $WVX$ have the same shape and size. The transformation from $\triangle PQR$ to $\triangle WVX$ is a rotation of $180^{\circ}$ about the origin.

Answer:

a. $DEFG\cong JKLM$, by translating $DEFG$ down 2 units and right 2 units.
b. $\triangle ABC\cong\triangle UTS$, by reflecting $\triangle ABC$ across the $y$ - axis.
c. $\triangle PQR\cong\triangle WVX$, by rotating $\triangle PQR$ $180^{\circ}$ about the origin.