Chapter 8 Lesson 2 Objective: To identify similar polygons.

Notes Two figures that have the same shape but not necessarily the same size are similar (~). Similar Polygons Two figures are similar if: –Corresponding angles are congruent –Corresponding sides are proportional The ratio of the lengths of corresponding sides is the similarity ratio.

Example 1: Understanding Similarity ABCD ~ EFGH. Complete each statement. A B C D 53° E H FG 127° a.= 53 Corresponding angles are congruent. b. Corresponding sides are proportional.

∆ABC ~ ∆XYZ. Complete each statement. Example 2: Understanding Similarity AC B X Y Z 78° 42° a. Corresponding angles are congruent. b. Corresponding sides are proportional. = 78

Example 3: Determining Similarity Determine whether the triangles are similar. If they are, write a similarity statement and give the similarity ratio. Remember: Two figures are similar if: Corresponding angles are congruent Corresponding sides are proportional All three pairs of angles are congruent by the markings. ∆ABC ~ ∆FEDSimilarity Statement 3 : 4 or ¾ Similarity Ratio

Example 4: Determining Similarity Determine whether the triangles are similar. If they are, write a similarity statement and give the similarity ratio. X Y Z P N M Remember: Two figures are similar if: Corresponding angles are congruent Corresponding sides are proportional All three pairs of angles are congruent by the markings. ∆XYZ ~ ∆MNPSimilarity Statement 2 : 3 or 2 / 3 Similarity Ratio

Example 5: Determining Similarity Determine whether the parallelograms are similar. Explain. B A C D KL J M 120°100° They are not similar because corresponding angles are not congruent.

Example 6: Using Similar Figures LMNO ~ QRST. Find the value of x. Step 1: Write a proportion. Step 2: Substitute. Step 3: Cross Multiply.

Example 7: Using Similar Figures LMNO ~ QRST. Find the value of SR. Step 1: Write a proportion. Step 2: Substitute. Step 3: Cross Multiply.

Assignment Pg. 425 #1-16; 21-28; 32-39