Geometry

1. Geometry 7.5 Theorems for Similar Triangles

2. Two Triangles can be proved similar by using: • Definition of similar polygons • All angles congruent • All sides proportional • AA Postulate (2 angles = 2 angles) Today we learn 2 additional methods: • SAS Similarity Theorem • SSS Similarity Theorem

3. SAS Similarity Theorem If an angle of one triangle is congruent to an angle of another triangle and the sides including those angles are in proportion, then the triangles are similar. D ∆ABC ~ ∆DEF A 6 8 4 m<A = m<D 3 3 4 small = B C big E 6 8 F

4. SSS Similarity Theorem If the sides of two triangles are in proportion, then the triangles are similar. ∆ABC ~ ∆DEF D 4 6 8 small = = A big 6 9 12 6 9 6 4 B C E 8 12 F

5. 4. 2. 3. A A 10 6 80 E D E D 3 80 5 C B B C L R F 3 5 16 24 20 10 M K N 6 6 H X S G 32 15 10 6 O R Q F 60 10.5 9 70 40 H G 70 P R X S S T 6 7 80 Problems: State the Method and Similarity Statement

6. A B X C D 1. Given: Prove: AB || DC

7. C Y A X B 2. Given: Prove:

8. Homework pg. 264 CE #1-6 WE #1-13

9. Similarity Chart All Polygons Triangles • Definition: • All angles congruent • All sides proportional • AAPostulate (2 <‘s = 2 <‘s) • SAS Similarity Theorem • SSS Similarity Theorem

10. Properties of Similar ∆’s • Similarity has some of the same properties as equality and congruence. • These properties include: REFLEXIVE SYMMETRIC TRANSITIVE

11. Name 2 similar ∆’s. Justify with a theorem. E 10 B 6 C 15 9 A D ∆ABC ~ ∆DEC by SAS Similarity ∆FHG ~ ∆XRS by SSS Similarity R F 20 16 24 10 H 15 G X 32 S

12. Name 2 similar ∆’s. Justify with a theorem or postulate. A 80˚ D E 80˚ B C ∆CDE ~ ∆CAB by SAS Similarity ∆ADE ~ ∆ABC by AA Postulate C 6 10 D E 5 3 B A

13. From the homework pg. 266 #3, 12