1. G.14 The student will use similar geometric objects in two- or three-dimensions to a. compare ratios between side lengths, perimeters, areas, and volumes; b. determine how changes in one or more dimensions of an object affect area and/or volume of the object; c. determine how changes in area and/or volume of an object affect one or more dimensions of the object; and d. solve real-world problems about similar geometric objects.

2. Similar Figures figures that have the same shape but not necessarily the same size. -All Spheres are Similar!

3. Similar Solids3 16 12 8 6 9 Are these solids similar? Example:

4. Similar Solids4 16 12 8 6 9 All corresponding ratios are equal, so the figures are similar Are these solids similar? Example: Solution:

5. Similar Solids5 8 18 4 6 Are these solids similar? Example:

6. Similar Solids6 8 18 4 6 Corresponding ratios are not equal, so the figures are not similar. Are these solids similar? Solution: Example:

7. Scale Factors used to compare perimeters, areas, and volumes of similar two-dimensional and three-dimensional geometric figures. A change in one dimension of an object results in changes in area and volume in specific patterns

8. Ratio of Perimeters If two polygons are similar, their corresponding sides, altitudes, medians, diagonals, angle bisectors and perimeters are all in the same ratio. Example: If the sides of two similar triangles are in the ratio 4:9, what is the ratio of their perimeters?

9. Ratio of Area If two polygons are similar, the ratio of their areas is equal to the square of the ratio of their corresponding sides. This applies to Lateral, Base, and Surface area Example: If the sides of two similar triangles are in the ratio of 3:5, find the ratio of their areas.

10. Similar Solids10 4 Similar Solids and Ratios of Areas Find the ratio of the sides. Surface Area = base + lateral = 40 + 108 = 148 5 2 4 3.5 Surface Area = base + lateral = 10 + 27 = 37 Ratio of surface areas: 148:37 = 4:1 = 2 2 : 1 2 8 7

11. Ratio of Volume If two polygons are similar, the ratio of their volumes is equal to the cube of the ratio of their corresponding sides. Example: If the sides of two similar triangles are in the ratio of 2:3, find the ratio of their volumes.

12. Example The volume of two spheres are in a ratio of 8:64. What is the ratio of their radii?