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Start by identifying the corresponding vertices on the graph.
Angles: ∠ W ≅ ∠ Q, ∠ X ≅ ∠ R, ∠ Y ≅ ∠ S, ∠ Z ≅ ∠ T
Sides: WX/QR = XY/RS = YZ/ST = ZW/TQ
Two polygons are similar if their corresponding angles are congruent and if the lengths of the corresponding sides are proportional. We are given that WXYZ ~ QRST.
We can identify the pairs of congruent angles by matching them using the order they appear in the similarity statement. ccccc W & X & Y & Z ↓ & ↓ & ↓ & ↓ Q & R & S & T The extended proportion that relates the corresponding sides for the similar polygons is created by writing a series of ratios for the corresponding side lengths. Let's list the pairs of congruent angles and write the ratios of the corresponding side lengths in a statement of proportionality.
| Angles | Sides |
|---|---|
| ∠ W ≅ ∠ Q ∠ X ≅ ∠ R ∠ Y ≅ ∠ S ∠ Z ≅ ∠ T | WX/QR = X Y/R S = YZ/ST = ZW/TQ |