Similarity

50

4040

3030303030

2020202020

1010101010

Indirect Measurement

SSS~, SAS~, AA~

Similarity Ratio

Similarity Statements

Proportions

You want to produce a scale drawing of your living room, which is 24 ft by 15 ft. If you use a scale of 4 in. = 6 ft, what will be the dimensions of your

scale drawing?

10 in. by 16 in.10 in. by 16 in.

3y 8

12y

5

3.13340

or

A model is built having a scale of 1 : 100,000. How high would a

35,600-ft mountain be in the model? Give your answer to the nearest tenth

of an inch.

.36.36

On a blueprint, the scale indicates that 6 cm represent 15 feet. What is the

length of a room that is 9 cm long and 4 cm wide on the blueprint?

22.5 ft. by 10 ft.22.5 ft. by 10 ft.

n 6

3nn 5

3n 1

-3-3

Write a similarity statement for the triangles.

FGHCDE ~

State whether the triangles are State whether the triangles are similar. If so, write a similarity similar. If so, write a similarity

statement.statement.

∆∆ABC ~ ABC ~ ∆MNO∆MNO

State whether the triangles are State whether the triangles are similar. If so, write a similarity similar. If so, write a similarity

statement.statement.

∆ABD ~ ∆CBD

In ∆ QRS, QR = 16, RS = 64, and m R = 29. In ∆UVT, VT = 8, TU = 32, and m T = 29.

State whether the triangles are State whether the triangles are similar. If so, write a similarity similar. If so, write a similarity

statement.statement.

∆QRS ~ ∆UVT

A model is made of a car. The car is 9 feet long and the model is 6 inches long. What is the ratio of the length of the car to the length of the model?

18:118:1

The Sears Tower in Chicago is 1450 feet high. A model of the tower is 24 inches tall. What is the ratio of the height of the model to the height of the actual Sears Tower?

1:7251:725

In ∆RST, RS = 10, RT = 15, and m R = 32. In ∆UVW, UV = 12, UW = 18, and m U = 32.

Are the polygons similar? If they are, write a similarity statement and give the similarity ratio.

RST UVW5

6

Explain why the triangles are similar. Then find the value of

x.

AAAA~~ 3

24

Explain why the triangles are similar. Then find the value of

x.

AAAA~~ 3

113

Are the triangles similar? If so, explain why.

AAAA~~

Campsites F and G are on opposite sides of a lake. A survey crew made the measurements shown on the diagram. What is the distance between the two campsites? The diagram is not to scale.

42.3 m42.3 m

Use the information in the diagram to determine the height of the tree to the

nearest foot.

80 ft80 ft

Michele wanted to measure the height of her school’s flagpole. She placed a mirror on the ground 48 feet from the flagpole, then walked backwards until she was able to see the top of the pole in the mirror. Her eyes were 5 feet above the ground and she was 12 feet from the mirror. Using similar triangles, find the height of the flagpole to the nearest tenth of a foot.

20 ft20 ft