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Five-Minute Check (over Lesson 4–8)Main Idea and VocabularyExample 1:Use Shadow ReckoningExample 2:Use Indirect Measurement

• indirect measurement

• Solve problems involving similar triangles.

Use Shadow Reckoning

TREES A tree in front of Marcel’s house has a shadow 12 feet long. Marcel’s shadow is 3 feet long. If Marcel is 5.5 feet tall, how tall is the tree?

Use Shadow Reckoning

Answer: The tree is 22 feet tall.

tree’s shadow tree’s heightMarcel’s shadow Marcel’s height

12 ● 5.5 = 3 ● h Find the cross products.

Multiply.

Simplify.

Divide each side by 3.

1. A2. B3. C4. D

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A. 4.5 feet

B. 5 feet

C. 5.5 feet

D. 6 feet

Jayson casts a shadow that is 10 feet long. At the same time, a flagpole casts a shadow that is 40 feet long. If the flagpole is 20 feet tall, how tall is Jayson?

Use Indirect Measurement

SURVEYING The two triangles shown in the figure are similar. Find the distance d across the stream.

Use Indirect Measurement

Answer: The distance across the stream is 16 meters.

Write a proportion.

AB = 48, ED = d, BC = 60, and DC = 20

Multiply. Then divide each side by 60.

48 ● 20 = d ● 60 Find the cross products.

Simplify.

1. A2. B3. C4. D

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A. 6 feet

B. 6.5 feet

C. 7 feet

D. 7.5 feet

SURVEYING The two triangles shown in the figure are similar. Find the distance d across the stream.

End of the Lesson

Five-Minute Check (over Lesson 4–8)

Image Bank

Math Tools

Solving Proportions

Dilations

Similar Triangles

1. A2. B3. C4. D0% 0%0%0%

(over Lesson 4-8)

Find the coordinates of the image of the parallelogram ABCD after a dilation with a scale factor of 2. Parallelogram ABCD has vertices at A(1, 1), B(3, 3), C(6, 3), D(4, 1).

A. A′(2, 2), B′(6, 6), C′(12, 6), D′(8, 2)B. A′(1, 2), B′(5, 6), C′(12, 12), D′(8, 2)C. A′(6, 6), B′(2, 2), C′(12, 6), D′(2, 8)D. A′(2, 2), B′(6, 6), C′(6, 12), D′(8, 2)

1. A2. B3. C4. D

(over Lesson 4-8)

A.

B.

C.

D.

0% 0%0%0%

1. A2. B3. C

0% 0%0%

(over Lesson 4-8)

Parallelogram ABCD has vertices at A(1, 1), B(3, 3), C(6, 3), D(4, 1). Identify whether the image of parallelogram ABCD after a dilation with a scale factor of 2 is an enlargement or a reduction.

A. enlargementB. reductionC. cannot be determined

1. A2. B3. C

(over Lesson 4-8)

A. enlargementB. reductionC. cannot be

determined

1. A2. B3. C4. D

0% 0%0%0%

(over Lesson 4-8)

Triangle M is similar to triangle N. What scale factor was used to dilate triangle N to M?

A. 3

B. 2

C.

D.