1. 13.4 Congruent and Similar Solids
Objective:
Students will identify congruent or similar solids.

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

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

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

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

6. Theorem 13.1
If 2 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
Example: The radii of 2 similar spheres are 3 and 4.
Scale factor = 3:4
Ratio of surface areas = 9:16
Ratio of volumes = 27:64

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