1. EXAMPLE 3
Standardized Test Practice

2. EXAMPLE 3
Standardized Test Practice
SOLUTION
The flagpole and the woman form sides of two right triangles with the ground, as shown below. The sun’s rays hit the flagpole and the woman at the same angle. You have two pairs of congruent angles, so the triangles are similar by the AA Similarity Postulate.

3. Standardized Test Practice
EXAMPLE 3
Standardized Test Practice
You can use a proportion to find the height x. Write 5 feet 4 inches as 64 inches so that you can form two ratios of feet to inches.
x ft
64 in.
50 ft
40 in. =
Write proportion of side lengths.
40x = 64(50)
Cross Products Property
x = 80
Solve for x.
The flagpole is 80 feet tall. The correct answer is C.
ANSWER

4. GUIDED PRACTICE
for Example 3 4.
What If ? A child who is 58 inches tall is standing next to the woman in Example 3. How long is the child’s shadow?
58 in. x 80
50 ft.

5. You can use a proportion to find the length of the shadow (x).
GUIDED PRACTICE
for Example 3
SOLUTION
The flagpole and the child next to the women form sides of two right triangles with the ground, here, there are two pairs of congruent angles, so the triangles are similar by the AA similarity postulate.
You can use a proportion to find the length of the shadow (x). 58 x = 80 50
Write proportion of side length
80x =
Cross product property
x = 36.25
Solve for x

6. GUIDED PRACTICE
for Example 3
The length of the shadow is in. long.
ANSWER

7. GUIDED PRACTICE
for Example 3 5.
You are standing in your backyard, and you measure the lengths of the shadows cast by both you and a tree. Write a proportion showing how you could find the height of the tree.
SOLUTION
Tree height
Your height =
Length of your shadow
Length of shadow