∆ Identify congruent or similar solids. ∆ State the properties of similar solids.

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

5cm 20cm 15cm 6cm 8cm 2cm The ratio of the measures is called the scale factor.

∆ Solids that 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 ∆ The volumes are equal.

¬ ¬ 8√ 7 cm 16 cm 8√ 3 cm 4√ 7 cm 8 cm 4√ 3 cm ¬ 15 in 8 in 17 in ¬ 12 in5 in 13 in

Determine whether the REGULAR pentagonal pyramids are similar, congruent, or neither. ¬ ¬ 8√ 7 cm 16 cm 8√ 3 cm 4√ 7 cm 8 cm 4√ 3 cm

¬ ¬ 8√ 7 cm 16 cm 8√ 3 cm 4√ 7 cm 8 cm 4√ 3 cm 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 8√ 3 cm 4√ 3 cm 16 cm 8 cm 8√ 7 cm 4√ 7 cm 2 The ratios of the measures are equal, so we can conclude that the pyramids are similar.

¬ 15 in 8 in 17 in ¬ 12 in5 in 13 in Determine whether the cones are similar, congruent, or neither. Radius of larger cone Radius of smaller cone Height of larger cone Height of smaller cone Since the ratios are not the same, there is no need to find the ratio of the slant heights. The cones are not similar.

If two solids are similar with a scale factor of a:b, then the surface areas have a ratio of a²:b², and the volumes have a ratio of a³:b³. ¬ ¬ ∆ Scale Factor 3:2 ∆ Ratio of surface areas 3²:2² or 9:4 ∆ Ratio of volumes 3³:2³ or 27:8

Volleyballs are spheres. One ball has a diameter of 4 inches, and another has a diameter of 20 inches. Find the scale factor of the two volleyballs Diameter of the smaller sphere Diameter of the larger sphere Simplify 1515 The scale factor is 1:5

Find the ratio of the surface areas of the two spheres. Surface area of smaller sphere Surface area of larger sphere a² 1² b² 5² 1 Simplify 25 The ratio of the surface areas is 1:25

Find the ratio of the volumes of the two spheres. Volume of the smaller sphere Volume of the larger sphere a³ b³ 1³ 5³ 1 Simplify 125 The ratio of the volumes of the two spheres is 1:125.

∆ Pg. 710 ∆ 5-16,18-23, By: Kristen Miller and Erin Fields 1 st hr. ALL