Question

figure abcd is congruent to figure ghef as shown. which two - sides must be the same length? a. $overline{ab}$ and $overline{ef}$ b. $overline{da}$ and $overline{ab}$ c. $overline{bc}$ and $overline{fg}$ d. $overline{eh}$ and $overline{hg}$ e. $overline{dc}$ and $overline{fe}$

Explanation:

Step1: Recall congruent - figure property

In congruent figures, corresponding sides are equal.

Step2: Identify corresponding sides

Since figure $ABCD$ is congruent to figure $GHEF$, side $\overline{AB}$ corresponds to side $\overline{EF}$, side $\overline{BC}$ corresponds to side $\overline{FG}$, side $\overline{CD}$ corresponds to side $\overline{GH}$, and side $\overline{DA}$ corresponds to side $\overline{HE}$.

Answer:

A. $\overline{AB}$ and $\overline{EF}$
C. $\overline{BC}$ and $\overline{FG}$
E. $\overline{DC}$ and $\overline{FE}$ (because $\overline{DC}$ corresponds to $\overline{GH}$ and $\overline{FE}$ corresponds to $\overline{GH}$ as well in the congruent - figure relationship)