LEARNING GOALS – LESSON 7:2 Warm Up 1. If ∆QRS  ∆ZYX, identify the pairs of congruent angles and the pairs of congruent sides. Solve the proportion. 2. LEARNING GOALS – LESSON 7:2 7.2.1: Identify similar polygons. 7.2.2: Apply properties of similar polygons to solve problems. Figures that are _______________ (____) have the same shape but not necessarily the same size. Similar Polygons Definition Diagram Statements Two polygons are similar polygons if and only if their corresponding angles are congruent and their corresponding sides are proportional. ABCD~WXYZ ∠A ≅ ∠W ∠B ≅ ∠X ∠C ≅ ∠Y ∠D ≅ ∠Z A B C D Y X W Z

EXAMPLE 1A: DESCRIBING SIMILAR POLYGONS Identify the pairs of congruent angles and corresponding sides. A. B. 0.5 A ________________ ___________ is the ratio of the lengths of the corresponding sides of two similar polygons. A ________________ _______________ is a statement using symbols indicating that two figures are similar. Example:

EXAMPLE 1B IDENTIFYING SIMILAR POLYGONS A. Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement. Step 1 Identify pairs of congruent angles. Step 2 Compare corresponding sides. B. Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement. Step 1 Identify pairs of congruent angles. Step 2 Compare corresponding angles. C. Determine if ∆JLM ~ ∆NPS. If so, write the similarity ratio and a similarity statement. Step 1 Identify pairs of congruent angles. Step 2 Compare corresponding angles.

EXAMPLE 2: HOBBY APPLICATION Find the length of the model to the nearest tenth of a centimeter. A boxcar has the dimensions shown. A model of the boxcar is 1.25 in. wide. Find the length of the model to the nearest inch.