11 8 Congruent and Similar Solids Objectives To

11 -8 Congruent and Similar Solids Objectives: • To identify congruent or similar solids. • To state the properties of congruent solids.

Vocabulary Similar Solids Scale Factor Congruent Solids

Similar Solids • Similar solids are solids that have exactly the same shape but not necessarily the same size.

Scale Factor • The ratio of the measures is called the scale factor.

Congruent Solids • If the ratio of the corresponding measurements of two solids is 1: 1, then the solids are congruent. • Congruent polyhedra are exactly the same shape and exactly the same size.

Example 1 • Determine if this pair of solids is similar, congruent, or neither.

Example 2 • Determine if this pair of solids is similar, congruent, or neither.

Theorem 11 -1 • If two solids are similar with a scale factor of a: b, then the surface areas will have a ratio of a 2: b 2, and the volumes have a ratio of a 3: b 3.

Example 3 • Some information about surface area and volume of two similar solids is given. Find the missing value. • Solid #1 Solid #2 • SA = 7 m 2 SA = 175 m 2 • V = 5 m 3 V=?

Example 4 • Some information about surface area and volume of two similar solids is given. Find the missing value. • Solid #1 Solid #2 • SA = ? SA = 108 m 2 • V = 16 m 3 V = 432 m 3

In-Class Examples

Homework 11 -8 Worksheet