Section 8-3 Similar TrianglesGEOMETRY

ENTRY TASK – TWO LEVELS Medium/Difficult

Medium:Given: ACB EDB and ∠ ∠Prove: ΔABC ΔEBDF

Homework Review

Short Cuts for Similar TrianglesAAASASSS

AA Similarity Postulate If two angles of one triangle are congruent to two angles of a second triangle, then the triangles are similar. This means that corresponding angles are

congruent and corresponding sides are proportional!

SAS Similarity Theorem If an angle of one triangle is congruent to an angle of a second triangle, and the sides that include the two angles are proportional, then the triangles are similar.

This means that corresponding angles are congruent and corresponding sides are proportional!

SSS Similarity Theorem If the corresponding sides of two triangles are proportional, then the triangles are similar.

This means that corresponding angles are congruent and corresponding sides are proportional!

Example 1• Explain why the triangles are similar and write a similarity

statement. Then find DE.

2418

16 12

10

Example 2 In the sunny desert a cactus casts a 9 foot shadow. At the same time a 6 foot tall person, standing next to the cactus, casts a 4 foot shadow. How tall is the cactus?

Example 3 Explain why the triangles are similar and write a similarity statement. Then find the value of x.

9

6

Example 4 A photograph measuring four inches wide and five inches long is enlarged to make a wall mural. If the mural is 120 inches wide, how long is the mural?

Example 4 – Proofs Using Triangle Similarity Given: PR = 2NP,

PQ = 2MP Prove:

Example 5 – Proofs Using Triangle Similarity

Given: and

Prove:

Homework Page 455 Problems: 7-13, 19, 23, 26