13 4 Congruent and Similar Solids Objective Students

13. 4 Congruent and Similar Solids Objective: Students will identify congruent or similar solids.

Similar Solids n Similar solids are solids that have exactly the same shape but not the necessarily the same size. n You can determine if two solids are similar by comparing the ratios of corresponding measures (the scale factor)

Find the scale factor for each pair of similar solids. 2: 1 3: 4 1: 2

Congruent Solids n Two solids are congruent if: n The corresponding angles are congruent n The corresponding edges are congruent n The corresponding faces are congruent n The volumes are equal

Determine whether each pair of solids is similar, congruent, or neither. similar congruent neither

Theorem 13. 1 n If 2 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 n Example: The radii of 2 similar spheres are 3 and 4. Scale factor = 3: 4 n Ratio of surface areas = 9: 16 n Ratio of volumes = 27: 64 n

Find the indicated ratio. n Two similar cubes have a scale factor of 5: 2. Find the ratio of their surface areas. n n The ratio of the surface areas of two hemispheres is 49: 81. Find their scale factor. n n 25: 4 7: 9 The ratio of the surface areas of two similar cones is 64: 121. Find the ratio of their volumes. n 512: 1331