Honors Geometry Section 8.2 B Similar Polygons

Two polygons are congruent iff they have exactly the same size and shape. Two polygons are similar iff they have exactly the same shape.

More formally, two polygons are similar iff their vertices can be paired so that: 1. corresponding angles are congruent 2. corresponding sides are proportional.

For corresponding sides to be proportional, the ratios of the corresponding sides must be equal.

To state that the polygons to the right are similar, we might write _______________ or _______________ These statements are called similarity statements.

List 2 (of the 5) pairs of congruent angles.

List 5 ratios that will be equal. A statement such as this is called a proportionality statement.

Example: In the figure above, AB = 15, JF = 21, FG = 30, GH = 14, DE = 18 and EA = 10. Find all missing lengths.

The scale factor of two similar polygons is the ratio of any pair of corresponding sides. For the figures above, the scale factor is equal to Note: You must write the scale factor in the same order as the similarity statement.

Example: and AB = 24, BC = 32 and YZ = 40 Example: and AB = 24, BC = 32 and YZ = 40. What segment can you find the length of and what is its length? What is the scale factor for this similarity?