Page 25 - Math Course 2 (Book 2)

Congruent and Similar Solids
Mo. 7

Lesson 5 congruent solids

congruent solids are exactly the same shape and
exactly the same size. They are a special case of
similar solids.
KEY CONCEPTS:
1. Identify congruent or similar solids. They have a scale factor of 1
2. State the properties of similar solids. 5

MO. 7 - L5a 6 6

Identifying Congruent and
Similar Solids 5

Vocabulary A-Z

Let us learn some vocabulary Key Concept

Similar and Congruent Solids
similar solids
Similar solids are solids that have exactly the Two solids are similar if the ratios of corresponding
same shape but not necessarily the same size. linear measure are proportional. Two solids are
congruent if:
You can determine if two solids are similar by • the corresponding angles are congruent,
comparing the ratios of corresponding linear • the corresponding edges are congruent,
measurements • the corresponding faces are congruent, and
• the volumes are equal.
Similar Solids

THEOREM 13.1

If two solids are similar with a scale factor of a:b,
2
20 cm 8 cm then the surface areas have a ratio of a : b , and
2
3
6 cm the volumes have a ratio of a : b 3
15 cm 2 cm Example
5 cm
Scale factor 3:2
Nonsimilar Solids 2 2
Ratio of surface areas 3 : 2 or 9:4
3
3
Ratio of volumes 3 : 2 or 27:8
10 ft 7 ft
9 6

12 ft 8 ft
12 ft 8 ft 6 4

6 4

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