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

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 radius and circumference of the earth! C = Syene, Egypt (now Aswan) A = Alexandria

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 Workbook pg 301 and 302 ALL

Honors: 7-3 Assignments Secondary Assignment: Primary Assignment: Due Tuesday Website: join.quizizz.com Codes: Period 2: 860637 Period 4: 079290 Period 6: 230112 Secondary Assignment: Textbook pg 486 – 487 #1 – 7,10, 19, 23, 24

Standard: 7-3 Assignments Primary Assignment: Due Website: join.quizizz.com Codes: Period 1: Period 5: Period 7: Secondary Assignment: Textbook pg 486 – 487 #1 – 7,10, 19