Question

if ifgh ≅ mnkl, what are the corresponding parts? select all that apply.

hi ≅ lm
∠i ≅ ∠m
fg ≅ nk
∠h ≅ ∠l

Explanation:

Step1: Recall congruent - polygon rules

When two polygons are congruent, their corresponding angles and sides are congruent. For congruent polygons $IFGH\cong MNKL$, the order of the vertices gives the correspondence.

Step2: Match corresponding angles

The first - named vertices of the congruent polygons give corresponding angles. So $\angle I\cong\angle M$, the second - named vertices give $\angle F\cong\angle N$, the third - named vertices give $\angle G\cong\angle K$, and the fourth - named vertices give $\angle H\cong\angle L$.

Step3: Match corresponding sides

The side between the first and second - named vertices of the first polygon corresponds to the side between the first and second - named vertices of the second polygon. So $\overline{IF}\cong\overline{MN}$, $\overline{FG}\cong\overline{NK}$, $\overline{GH}\cong\overline{KL}$, $\overline{HI}\cong\overline{LM}$.

Answer:

$\overline{HI}\cong\overline{LM}$, $\angle I\cong\angle M$, $\overline{FG}\cong\overline{NK}$, $\angle H\cong\angle L$