Exploring Similar Polygons
Overview
Similar polygons have the same shape but not necessarily the same size: their corresponding angles are congruent and their corresponding sides are proportional. The ratio of two corresponding sides is the scale factor, and once it is known, any missing side can be found with a proportion. The correspondence matters — a similarity statement lists the vertices in matching order, so the statement itself tells you which parts correspond.
Vocabulary
- Similar Polygons
- Two polygons are similar if their corresponding angles are congruent and their corresponding sides are proportional.
- Corresponding Parts
- The angles and sides of similar polygons that occupy the same position in each figure; a similarity statement lists vertices in corresponding order.
- Scale Factor
- The ratio of the lengths of corresponding sides of similar polygons (second figure to first figure, in the order named).
- Proportion
- An equation stating that two ratios are equal.
Main Ideas
- Similarity requires both conditions: corresponding angles congruent and corresponding sides proportional. One without the other is not enough.
- In the statement PQRS ~ ABCD, P corresponds to A, Q to B, and so on — read the matching pairs straight from the statement.
- To find a missing side, establish a proportion using a pair of known corresponding sides and the pair containing the unknown.
- All segments of similar figures are proportional — midsegments, angle bisectors, medians, altitudes, and perimeters all follow the same scale factor.
- To test whether two polygons are similar, verify every pair of corresponding sides is proportional (and the angles are congruent).
Lesson Notes
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Lesson Video
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Practice Problems
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