Chapter 7

SIMPLIFY:

20 12 3

20 = 4 5 = 2 5

12 3 12 3 3 3 3

4 3= =

MULTIPLY:

( 2 5 )2

(2 5 )2 = 4 25 = 4 5 = 20.

COMPLETE:

( ___ )2 + ( ___ )2 = ( ___ )2

leg1

leg2

hyp

(leg1)2 + (leg2)2 = (hyp)2

Pythagorean Theorem

Complete to form RIGHT triangles:

3, 4, ____ 5, 12, ____

6, 8, ____ 8, 15, ____

3, 4, 5 5, 12, 13 6, 8, 10 8, 15, 17

Given segment lengths a, b, c longest

Right c2 a2 + b2

Obtuse c2 a2 + b2

Acute c2 a2 + b2

Right c2 = a2 + b2

Obtuse c2 > a2 + b2

Acute c2 < a2 + b2

COMPLETE:

L = ____

H = ____

45

45

L = L

H = L 2

SOLVE:

x = _____

y = _____

8

x

y45

45

x = 8

y = 8 2

COMPLETE:

LL = _____

H = _____30

60

Ls

LL = Ls 3

H = 2 Ls

SOLVE:

x = _____

y = _____30

604

x

y

x = 4 3

y = 8

AREA OF EQUILATERAL TRIANGLES:

A = ½ ( ____ )( ____ )

A = ½ ( ____)( ____ )

A = ( ____ )2

( ____ )

A = ½ bh

A = ½ ap

A = s2 4

3

Find the area:

(Equilateral Triangle)

6 3

30

63

9

18

33

A = ½ bh

A = ½ (18)(9 )

A = 81

3

3

A = ½ ap

A = ½ (3 )(54)

A = 81

3

3

A = s2 4

A = (18)2

4

A = 81

3

3

3

AREA OF SQUARES:

A = ( ____ )2

A = ½ ( ____ )( ____ )

A = ½ ( ____ )( ____ )

A = s2 A = ½ ap A = ½ d1d2

side (s)

a

Find the area:

(Square)

10 2

10 210

10

20

A = s2

A = 202

A = 400

A = ½ ap

A = ½ (10)(80)

A = 400

A = ½ d1d2

A = ½ (20 )(20 )

A = 400

2 2

45

AREA OF REGULAR HEXAGONS:

A = ½ ( ____ )( ____ )

A = ½ ap

120

a60

Find the area:

8

(Regular Hexagon)

8

4 4

4 3

60

A = ½ ap

A = ½ (4 3)(48)

A = 96 3

AREA OF PARALLELOGRAMS:

A = ( ____ )( ____ )

A = bh

Base (b)

Height (h)

AREA OF ANY TRIANGLE:

A = ½ ( ____ )( ____ )

A = ½bh

base (b)

height (h)

Find the height:

6 6

4

h2 + 22 = 62

h2 = 32h = 32 = 4 2

6 6

4

2 2

h

AREA OF RIGHT TRIANGLES:

A = ½ ( ____ )( ____ )

A = ½ (l1)( l2)

leg (l1) leg (l2)

AREA OF RHOMBUSES:

A = ½ ( ____ ) ( ____ )

A = ½ (d1)(d2)

AREA OF TRAPEZOIDS:

A = ½ ( ____ ) ( ____ + ____ )

A = ½ (h)(b1 + b2)

base (b1)

base (b2)

height (h)

FOR CIRCLES:

Circumference = ( __ )( __ )( __ )

C = 2rπ

What fraction of the circumference is arc AB?

r

120o

A

B

120 = 1 360 3

AREA OF CIRCLES:

A = ( ____ )( ____ )2

A = πr2

What fraction of the circle is shaded?

450

r

45 = 1 360 8