## Geometry: Common Core (15th Edition)

Congruent angles: $\angle K ≅ \angle H$ $\angle L ≅ \angle G$ $\angle M ≅ \angle F$ $\angle N ≅ \angle D$ $\angle P ≅ \angle C$ Extended proportions: $\frac{KL}{HG} = \frac{LM}{GF} = \frac{MN}{FD} = \frac{NP}{DC} = \frac{PK}{CH}$
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: $\frac{KL}{HG} = \frac{LM}{GF} = \frac{MN}{FD} = \frac{NP}{DC} = \frac{PK}{CH}$