Similar Figures

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Show your work for each problem.

1.
Two figures are similar if they have the same _____ but not necessarily the same _____.
1. a)shape, size
2. b)area, perimeter
3. c)color, shape
4. d)size, shape
2.
Triangle ABC has sides 2, 3, and 4 cm. Triangle DEF has sides 4, 6, and 8 cm. What is the scale factor from ABC to DEF?
1. a)4
2. b)0.5
3. c)2
4. d)3
3.
If two similar rectangles have a scale factor of 3, and the smaller rectangle has a width of 4 cm, what is the width of the larger rectangle in cm?
4.
Which of the following pairs of shapes are ALWAYS similar?
1. a)Two rectangles
2. b)Two triangles
3. c)Two squares
4. d)Two parallelograms
5.
A map has a scale of 1:50000. If two cities are 3 cm apart on the map, what is the actual distance in km?
6.
Two similar triangles have sides in the ratio 2:5. If the perimeter of the smaller triangle is 18 cm, what is the perimeter of the larger triangle?
7.
Two similar rectangles have lengths of 6 cm and 15 cm. If the width of the smaller rectangle is 4 cm, what is the width of the larger rectangle in cm?
8.
If , what is ?
1. a)5
2. b)15
3. c)9
4. d)45
9.
A photo is 8 cm wide and 12 cm tall. It is enlarged so that the new width is 20 cm. What is the new height?
10.
In two similar triangles, the ratio of corresponding sides is 3:7. If the shortest side of the larger triangle is 21 cm, what is the shortest side of the smaller triangle in cm?
11.
Triangle PQR is similar to triangle XYZ. In triangle PQR: PQ = 5 cm, QR = 8 cm, PR = 6 cm. In triangle XYZ: XY = 10 cm. Find YZ.
12.
A flagpole casts a shadow 15 m long. At the same time, a 2 m tall person casts a shadow 3 m long. How tall is the flagpole?
13.
Two similar pentagons have a scale factor of 4. If the area of the smaller pentagon is 25 square cm, what is the area of the larger pentagon in square cm?
14.
Rectangles A and B are similar. Rectangle A is 3 cm by 5 cm. Which of the following could be the dimensions of Rectangle B?
1. a)4 cm by 6 cm
2. b)6 cm by 8 cm
3. c)9 cm by 15 cm
4. d)5 cm by 7 cm
15.
An architect creates a model of a building using a scale of 1:200. If the model is 45 cm tall, how tall is the actual building in meters?
16.
Two similar triangles have areas in the ratio 9:25. What is the ratio of their corresponding sides? (Enter as a simplified ratio like 3:5)