Looking at the angle markers on the polygons, we can tell that there are four pairs of congruent angles.
∠ A ≅ ∠ E
∠ B ≅ ∠ F
∠ C ≅ ∠ G
∠ D ≅ ∠ H
Comparing the Ratios
Now, let's compare the ratios of the corresponding sides. Recall that the included side between a pair of angles of one polygon corresponds to the included side between the corresponding pair of congruent angles of another polygon.
Corresponding Sides
Ratio
Substitute Lengths
Simplify
A B, E F
AB/EF
4/10
2/5
B C, F G
BC/FG
6/16
3/8
C D, G H
CD/GH
4/10
2/5
D A, H E
DA/HE
6/16
3/8
As we can see, the ratios are not equal. Therefore, the given polygons are not similar.
