Introduction to Similarity

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Show your work for each problem.

1.
Two figures are similar if they have:
1. a)Different shapes and different sizes
2. b)Both the same shape and the same size
3. c)The same shape but not necessarily the same size
4. d)The same size but not necessarily the same shape
2.
Which symbol is used to show that two figures are similar?
1. a)
2. b)
3. c)
4. d)
3.
If the scale factor from figure A to figure B is , and a side of figure A is cm, what is the length of the corresponding side of figure B (in cm)?
4.
Are all squares similar to each other?
1. a)Only if they are rotated the same way
2. b)No, because squares can be different sizes
3. c)Yes, because all squares have the same angles and proportional sides
4. d)Only if they are the same size
5.
Triangle Triangle . If cm and cm, what is the scale factor from to ? (Enter as a decimal)
6.
Two rectangles have sides of cm by cm and cm by cm. Are they similar?
1. a)No, because the ratios are not equal ()
2. b)Yes, because both have right angles
3. c)No, because they are different sizes
4. d)Yes, because both are rectangles
7.
Triangle Triangle . In : cm, cm, cm. In : cm. Find and .
8.
On a map with scale 1:50000, two cities are 6 cm apart. What is the actual distance between them in kilometers?
9.
An architect creates a 1:100 scale model of a building. The model is 45 cm tall and 30 cm wide. Find the actual building's height and width in meters.
10.
In similar triangles and , cm, cm, and cm. Find (in cm).
11.
Triangle has angles , , and . Triangle has angles , , and an unknown angle. Are they similar? Find the unknown angle.
12.
If the scale factor from triangle A to triangle B is , what can we conclude?
1. a)Triangle B is smaller than triangle A
2. b)The triangles are not similar
3. c)The triangles are congruent
4. d)Triangle B is larger than triangle A
13.
A flagpole casts a shadow of 12 meters. At the same time, a 2-meter stick casts a shadow of 3 meters. How tall is the flagpole?
14.
If with a scale factor of , and side cm, what is side (in cm)?
15.
Which of the following pairs of shapes are ALWAYS similar to each other?
1. a)Two circles
2. b)Two rectangles
3. c)Two triangles
4. d)Two parallelograms