7.3 Similar Triangles Then: You used AAS, SSS, and SAS

Congruence Theorems to prove triangles congruent.

Now: 1. Identify similar triangles using the AA Similarity Postulate and the SSS and SAS Similarity Theorems.

2. Use similar triangles to solve problems.

http://brettedwards.com/wp-content/uploads/2012/01/pyramid2.jpg

Postulate 7.1

Example 1: Use AA Similarity Postulate

Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning.

a. b.

Theorems 7.1 & 7.2

Example 2 : Use SSS and SAS Similarity Theorems

Determine whether the triangles are similar. If so, write a similarity statement. Explain your reasoning.

a.

Example 2:b.

Example 3: Sufficient Conditions

Given ΔABC and ΔDEC, which of the following would be sufficient information to prove the triangles are similar?

A. =

B. mA = 2mD

C. =

D. =

Theorem 7.4

A C

B F

E

D

Z

Y

X

Example 4: Parts of Similar Triangles

Identify the similar triangles. Find the measure.a. IU

Example 4: Parts of Similar Triangles

Identify the similar triangles. Find the measure.b. AC

Example 5: Indirect Measurement

SKYSCRAPERS Josh wanted to measure the height of the Sears Tower in Chicago. He used a 12-foot light pole and measured its shadow at 1 p.m. The length of the shadow was 2 feet. Then he measured the length of Sears Tower’s shadow and it was 242 feet at the same time. What is the height of the Sears Tower?

Example 5: Sears Tower

Step 1: To solve set up a proportion using words:

___________________ = ___________________

Step 2: Substitute the values that are known and solve

for the unknown.________= ________

Example 5: Indirect Measurement

LIGHTHOUSES On her trip along the East coast, Jennie stops to look at the tallest lighthouse in the U.S. located at Cape Hatteras, North Carolina.At that particular time of day, Jennie measures her shadow to be 1 foot 6 inches in length and the length of the shadow of the lighthouse to be 53 feet6 inches. Jennie knows that her heightis 5 feet 6 inches. What is the height ofthe Cape Hatteras lighthouse to the nearest foot?

Example 5: Lighthouse

Step 1: To solve set up a proportion using words:

___________________ = ___________________

Step 2: Substitute the values that are known and solve

for the unknown.________= ________

7.3 Assignment:p. 483-487 #9-16 all, 18-22 evens,

28-34 evens,40, 46, 50, 52#28 – proof on handout#30 – graph on handout