Answer
Congruent angles:
$\angle K ≅ \angle H$
$\angle L ≅ \angle G$
$\angle M ≅ \angle F$
$\angle N ≅ \angle D$
$\angle P ≅ \angle C$
Extended proportions:
$\frac{KL}{HG} = \frac{LM}{GF} = \frac{MN}{FD} = \frac{NP}{DC} = \frac{PK}{CH}$
Work Step by Step
First, we identify all the pairs of congruent angles:
$\angle K ≅ \angle H$
$\angle L ≅ \angle G$
$\angle M ≅ \angle F$
$\angle N ≅ \angle D$
$\angle P ≅ \angle C$
Now, let's take a look at the corresponding sides in both pentagons. An extended proportion is given when at least several of the ratios are equal, as they are in similar polygons:
$\frac{KL}{HG} = \frac{LM}{GF} = \frac{MN}{FD} = \frac{NP}{DC} = \frac{PK}{CH}$
