skyler cornaby and lyndon crouch 13-4 similar and congruent solids

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