Since all angles of a rectangle are right angles and all right angles are congruent, we know that the corresponding angles must be congruent.
∠ P ≅ ∠ W
∠ Q ≅ ∠ X
∠ R ≅ ∠ Y
∠ S ≅ ∠ Z
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
P Q, W X
PQ/WX
15/10
3/2
Q R, X Y
QR/XY
9/6
3/2
R S, Y Z
RS/YZ
15/10
3/2
S P, Z W
SP/ZW
9/6
3/2
As we can see, all of the ratios are equal. Therefore, the given polygons are similar and the scale factor is 32.
PQRS ~ WXYZ
