Chapter 8

2 34 6

The means are _____

The extremes are ____

___ ___=

Means: 3 and 4

Extremes: 2 and 6

In a proportion, the product of the _____

equals the product of the _____

In a proportion, the product of the means equals

the product of the extremes

What symbol is used for “similar”?

~

For similar polygons,

corresponding angles are ____ and

corresponding sides are ____

For similar polygons,

corresponding angles are congruent

and

corresponding sides are proportional

If DOG ~ CAT then

D ~ ___ and G ~ ____= =

If DOG ~ CAT then

D C and G T= =~ ~

Always, sometimes or never?

Two congruent polygons are _____ similar

Two congruent polygons are always similar

Always, sometimes or never?

Two rectangles are

_____ similar

Two rectangles are sometimes similar

The ratio of the length:width of a Golden Rectangle

is (approximately)

_____ : _____

The ratio of the length:width of a Golden Rectangle

is (approximately)

1.62 : 1

If BAD ~ CAT thencomplete the proportion:

A

B

DC

T

a b c = =

a

b

c

x

y

z

a b c y x z= =___ ___ ___

Complete the proportion:

3 4 x

3 4

8

15

xy

= =

3 4 x

3 4

8

15

xy

= =3 + y 12 15

(scale factor = 1:3)

Multiply (x + 3)(x – 5)

(x + 3)(x – 5)

= x2 – 5x + 3x – 15 F O I L

= x2 – 2x - 15

SOLVE BY FACTORING:

x2 – 9 = 0

x2 + 3x –18 = 0

x2 – 9 = 0(x – 3)(x + 3) = 0

x = 3 or -3

x2 + 3x –18 = 0(x + 6)(x – 3)= 0

x = -6 or 3

Complete the proportion:

10 5

x__ __=

10 x x 5

=

hyp1 alt

alt hyp2

_____ _____=

__ __

Complete the proportion:

10 5

y __ __=

10 y y 15

=

hyp1 leg1

leg1 hyp_____ _____=

__ __

Complete the proportion:

10 5

z__ __=

5 z z 15

=

hyp2 leg2

leg2 hyp_____ _____=

__ __

Find the Geometric Mean of 4 and 8

(4)(8) 32 4 2= =

(Square root of product)

Complete the proportion:

a b

___ ___=

a b

x y

a b

___ ___=

a b

x y

xy

Complete the proportion:

a b

___ = ___?

?

a

b

c

d

___ = ___

a

b

c

d

cd

ab

For similar polygons, the ratio of

perimeters equals the _________

For similar polygons, the ratio of perimeters equals the scale factor

Complete for similar polygons/circles:

Scale Factor = 2 : 3

Perimeter/Circumference Ratio = _____

Area Ratio = _____

Perimeter Ratio = 2 : 3

Area Ratio = 4 : 9 (22 : 32)