7-3: Proving Triangles are Similar Rigor: 1) Prove 2 triangles are similar 2) Use similar triangles to solve indirect measurement problems Relevance : Logic and proof, indirect measurement

Similarity Recap: Finish the sentence  Two figures are similar if there is one or more ________________ that will map one figure onto the other.  The 4 similarity transformations are ________  The corresponding angles of similar figures are ______  The corresponding side lengths of similar figures are ____  The corresponding sides of dilated figures are __________

3 Triangle Similarity Criterion  (AA ~) – If 2 pairs of corresponding angles are congruent, the ∆s are ~.  (SSS ~) – If all corresponding sides are proportional, the ∆s are ~.  (SAS ~) – If 2 pairs of corresponding sides are proportional and the included angle pair is congruent, the ∆s are ~.

Dissecting Similarity Statements  Turn to core book page 298  Complete example 2 and the reflection problems on your own.  Be ready to discuss reflection questions in a few minutes

EX 1: Are the triangles similar? Justify your answer.

EX 2: Prove that the triangles are similar. A) B)

EX 3:

Indirect Measurement: One of my favorite applications of Geometry!  One method of indirect measurement is using similarity proportions of triangles!  Used to calculate the height of pyramids & mountains, width of rivers, etc.  Ancient Greek philosopher Eratosthenes even used similar triangles to approximate the circumference of the earth!

EX 4: What is the height of the cliff?

EX 5: Using Indirect Measurement A birdbath 2ft 6in tall casts an 18in shadow in a garden at the same time an oak tree casts a 90ft shadow. How tall is the tree?

7-3 Classwork from the textbook  Heading: 7-3 CW pg 486  Problems: #2 – 10 evens, 16 – 18, 23, Homework from the core book  Page 301 and 302 ALL  Due Thurs/Fri