1. Obj. 35 Triangle Similarity The student is able to (I can): Identify similar polygons Prove certain triangles are similar by using AA~, SSS~, and SAS~ Use triangle similarity to solve problems.

2. similar polygonsTwo polygons are similar if and only if their corresponding angles are congruent and their corresponding side lengths are proportional. Example: 6N5 3MO4 L12X810EN X L S E A O MS6A3 4 5 6 = = = 6 8 10 12 NOEL ~ XMAS 3. Note: A similarity statement describes two similar polygons by listing their corresponding vertices. Example: NOEL ~ XMAS Note: To check whether two ratios are equal, cross-multiply themthe products should be equal. Example:3 4 = 6 8 24 = 24 4. ExampleDetermine whether the rectangles are similar. If so, write the similarity ratio and a similarity statement. Q15U6 DA R25E10 TCAll of the angles are right angles, so all the angles are congruent. QUAD ~ RECT 6 15 = ? sim. ratio: 3 10 25 5 150 = 150 5. Angle-Angle Similarity (AA~) If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. P MADC OM P A O Therefore, MAC ~ POD by AA~ 6. Side-Side-Side Similarity (SSS~) If the three sides of one triangle are proportional to the three corresponding sides of another triangle, then the triangles are similar. N 18W123024H 40O 16Y TWH HY WY = = NO OT NTTherefore, WHY ~ NOT by SSS~ 7. Side-Angle-Side Similarity (SAS~) If two sides of one triangle are proportional to two sides of another triangle, and the included angles are congruent, then the triangles are similar. E U 52.5 L2VLU LV = TE TXT4XL TTherefore, LUV ~ TEX by SAS~ 8. ExampleExplain why the triangles are similar and write a similarity statement. X 34LE 56UV T90 56 = 34 Therefore mV = mX, thus V X. Since mU = mE = 90, U E Therefore, LUV ~ TEX by AA~ 9. ExampleVerify that SAT ~ ORT R 20 S12 15T 16OAATS RTO (Vertical angles ) 12 15 = ? 16 20 240 = 240 Therefore, SAT ~ ORT by SAS~