1. By: David Samkutty and Viet Tran Blah ™

2. Objectives Identify Congruent or Similar Solids State the properties of similar solids

3. Similar Solids Similar solids are solids that have the exactly the same shape but not necessarily the same size. You can determine if two solids are similar by comparing the ratios of corresponding linear measurements.

4. Similar Solids 4 in 2 in 1 in 2in 3 in 6 in. In the similar solids below, the scale factor is 4/2=6/3=2/1

5. Congruent Solids Congruent solids are exactly the same shape and exactly the same size. They have a scale factor of 1. Two solids are congruent if: The corresponding angles are congruent, The corresponding edges are congruent, The corresponding faces are congruent, and Volumes are equal

6. Example 1 6√7 in 3√7 in 10 in 20 in 8√3 in 4√3 in Base edge of larger pyramid Base edge of smaller pyramid Height of larger pyramid Height of smaller pyramid Lateral edge of larger pyramid Lateral edge of smaller pyramid

7. Explanations Base Edge = 8√3 = 2 4√3 Height = 20 = 2 10 Lateral Edge= 6√7 = 2 3√7 The two pyramids are similar with a scale factor of 2

8. Example 2 Radius of larger cone = 8 height of larger cone = 15 Radius of smaller cone 5 height of smaller cone 12 5 in 17 in 15 in 13 in 12 in 8 in Since the ratios aren’t the same, there’s no need to find the ratio of the slant heights. The cones are not similar.

9. Theorem 13.1 If two solids are similar with a scale factor of a:b, then the surface areas have a ratio of a 2 :b 2, and the volumes have a ratio of a 3 :b 3. Scale Factor 3:2 Ratio of T 3 2 :2 2 or 9:4 9 Ratio of V 3 3 :2 3 or 27:8 6 6 6 4 4

10. Assignments Pg. 711 # 11 – 16, 18-23, 27-30