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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

Study Guide and Review

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Exercise 38 Page 874

Similar solids have the same shape and all of their corresponding dimensions are proportional. The ratio of corresponding linear dimensions of two similar solids is the scale factor. If the scale factor is 1:1 they are also congruent.

Similar, Congruent, or Neither? Similar
Scale Factor: 1:4

Practice makes perfect

Similar solids have the same shape and all of their corresponding dimensions are proportional. The ratio of corresponding linear dimensions of two similar solids is the scale factor. If the scale factor is 1:1 they are also congruent. Consider the given cubes.

Let's see whether the corresponding linear dimensions are proportional.

4/8 ? =4/8? =4/8

a/b=.a /4./.b /4.

1/4=1/4=1/4

The ratios of the corresponding measures are equal, so the cubes are similar. The scale factor is 1:4. Since the scale factor is not 1:1, the solids are not congruent.

Subchapter links

1 Representations of Three-Dimensional Figures p.872

2 Surface Areas of Prisms and Cylinders p.872

3 Surface Areas of Pyramids and Cones p.872

4 Volumes of Prisms and Cylinders p.873

5 Volumes of Pyramids and Cones p.873

6 Surface Areas and Volumes of Spheres p.873

7 Spherical Geometry p.874

8 Congruent and Similar Solids p.874