Skyler Cornaby and Lyndon Crouch 13-4 SIMILAR AND CONGRUENT SOLIDS.
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Transcript of Skyler Cornaby and Lyndon Crouch 13-4 SIMILAR AND CONGRUENT SOLIDS.
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Skyler Cornaby and Lyndon Crouch
13-4 SIMILAR AND CONGRUENT SOLIDS
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Objectives Identify congruent or similar solids State the properties of similar solids
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Definitions of similar and congruentVolume formulas for solids
Scale factorProportions
NEED TO KNOW
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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
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EXAMPLE #1Corresponding angles congruent
Corresponding edges congruent
Corresponding faces congruent
Volumes equal
2
2
2
2
22
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*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?
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*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.
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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
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Example #3These two cylinders are similar. Using
theorem 13.1 solve for the volume of the larger cylinder.
6
147
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Example #3 cont’d
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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?
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EXAMPLE #4 CONT’D
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Assignment
O Pg. 711 11-26, 36-39