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Definitions of similar and congruent Volume formulas for solids Scale factor Proportions NEED TO KNOW
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Skyler Cornaby and Lyndon Crouch
13-4 SIMILAR AND CONGRUENT SOLIDS
Objectives Identify congruent or similar solids State the properties of similar solids
Definitions of similar and congruentVolume formulas for solids
Scale factorProportions
NEED TO KNOW
Key Concept Two solids are congruent if
The corresponding angles are congruent The corresponding edges are congruent The corresponding faces are congruent The volumes are equal
EXAMPLE #1Corresponding angles congruent
Corresponding edges congruent
Corresponding faces congruent
Volumes equal
2
2
2
2
22
*Example #2*Lyndon is buying a new cage for his hedgehog and he want to buy a cage similar to his original cage. The smaller cage is 10in.X7in.X6in. The larger cage is 20in.X14in.X15in. Are the cages similar?
*Example # 2 cont’d*Length ratio-10:20 or 1:2*Width ratio-7:14 or 1:2*Height ratio-6:15 or 2:5*The cages are not similar because not all
the dimensional ratios are the same.
If two solids are similar with a scale factor of a:b then the surface area have a ratio of a2:b2, and the volumes, have a ratio of a3:b3.
Theorem 13.1
Scale factor 3:2Ratio of surface areas 32:22 or 9:4Ratio of volumes 33:23 or 27:8
10
8
1215
Example #3These two cylinders are similar. Using
theorem 13.1 solve for the volume of the larger cylinder.
6
147
Example #3 cont’d
EXAMPLE #4 Joey is trying to decide if his baseball
and his basketball are similar. If his baseball has a radius of 1.45 in. and his basketball has a radius of 4.7 in. Are they similar?
EXAMPLE #4 CONT’D
Assignment
O Pg. 711 11-26, 36-39