Proving Triangles Similar Related Topic Remember we had to prove triangles congruent? Proving triangles similar is similar to proving triangles congruent but different The theorems to prove triangles similar are different

Postulate 7.1 Angle-Angle similarity (AA~) Postulate If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar P T R S L M

Theorem 7.1 Side-Angle-Side Similarity (SAS~) Theorem If an angle of one triangle is congruent to an angle of a second triangle, and the sides including the two angles are proportional, then the triangles are similar Examples: Notice the difference

Theorem 7.2 Side-Side-Side (SSS~) Theorem If the corresponding sides of two triangles are proportional, then the triangles are similar Examples:

Are the triangles similar? Why? Write the similarity statement V S 45 45 R B

Are the triangles similar? Why? Write the similarity statement P X 8 6 Z Q R Y 4 3

If the triangles are similar, find DE 12 10 B 24 D C 16 18 E

Vocabulary Indirect measurement – You use similar triangles and measurements to find distances that are difficult to measure directly

Example of indirect measurement