Report

EXAMPLE 3

Standardized Test Practice

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.

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 = 50 ft

40 in.

64 in.

40x = 64(50)

x = 80

Write proportion of side lengths.

Cross Products Property

Solve for x.

ANSWER

The flagpole is 80 feet tall. The correct answer is C.

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?

ANSWER

36.25 in.

for Example 3

GUIDED PRACTICE

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.

SAMPLE ANSWER

tree height

your height

=

length of shadow

length of your shadow

EXAMPLE 3

Standardized Test Practice

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.

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 = 50 ft

40 in.

64 in.

40x = 64(50)

x = 80

Write proportion of side lengths.

Cross Products Property

Solve for x.

ANSWER

The flagpole is 80 feet tall. The correct answer is C.

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?

ANSWER

36.25 in.

for Example 3

GUIDED PRACTICE

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.

SAMPLE ANSWER

tree height

your height

=

length of shadow

length of your shadow

EXAMPLE 3

Standardized Test Practice

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.

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 = 50 ft

40 in.

64 in.

40x = 64(50)

x = 80

Write proportion of side lengths.

Cross Products Property

Solve for x.

ANSWER

The flagpole is 80 feet tall. The correct answer is C.

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?

ANSWER

36.25 in.

for Example 3

GUIDED PRACTICE

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.

SAMPLE ANSWER

tree height

your height

=

length of shadow

length of your shadow

EXAMPLE 3

Standardized Test Practice

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.

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 = 50 ft

40 in.

64 in.

40x = 64(50)

x = 80

Write proportion of side lengths.

Cross Products Property

Solve for x.

ANSWER

The flagpole is 80 feet tall. The correct answer is C.

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?

ANSWER

36.25 in.

for Example 3

GUIDED PRACTICE

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.

SAMPLE ANSWER

tree height

your height

=

length of shadow

length of your shadow

EXAMPLE 3

Standardized Test Practice

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.

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 = 50 ft

40 in.

64 in.

40x = 64(50)

x = 80

Write proportion of side lengths.

Cross Products Property

Solve for x.

ANSWER

The flagpole is 80 feet tall. The correct answer is C.

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?

ANSWER

36.25 in.

for Example 3

GUIDED PRACTICE

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.

SAMPLE ANSWER

tree height

your height

=

length of shadow

length of your shadow