Angle facts a º b º a º is the complement of b º P Q R S ^ PQRand ^ RQSAdd up to 90 º Two...

Angle facts

a º

b º

a º is the complement of b º

P

Q

R

S

^PQR and

^RQS Add up to 90 º

Two angles which make a RIGHT angle are

COMPLEMENTARY

and b º is the complement of a º

a º + b º = 90 º

the complements of the following angles are

10 º

50 º

35 º

17 º

81 º

45 º

36 º

57 º

6 º

A

B C

Dthe complement of < DBC is

E

< EBC = 72 º the size of <DBC is

the size of <ABD is

P14 ex 1A q 1,2,4,5,7 ex 1B

80 º

40 º

55 º

73 º

9 º

45 º

54 º

33 º

84 º

<ABD or

<EBC

18 º

72 º

Supplementary angles

E F G

H

p º q º

<EFH and <HFG add up to 180 º

Two angles which make a STRAIGHT angle

are

SUPPLEMENTARY

a º is the supplement of b º

and b º is supplement of a º

p º + q º = 180 º

the supplements of the following angles are

60 º 130 º 5 º

100 º 168 º 55 º

178 º 45 º 90 º

120 º

80 º

2 º

50 º

12 º

135 º

175 º

125 º

90 º

A

B

C

D

E

The supplement of <AED is

The supplement of <CED is

<AED IS140 º <AEB is

<DEC is 75 º <BEC is

<ABC

<CEB

40 º

105 º

P 16 EX 2A 1,2,5,6,7 AND EX 2B/C 1,2,3,4,

Vertically opposite angles

A B

CD

Vertically opposite angles are found on opposite sides of a vertex

< AEB IS VERTICALLY OPPOSITE <DEC

< AED IS VERTICALLY OPPOSITE <BEC

E

aº

bº

bº + aº = 180º

cº

bº + cº = 180º

aº must be equal to cº

<AEB and <DEC are vertically opposite angles

vertically opposite angles are equal

A

B

CD

E

Another pair of vertically opposite angles are

<AED and <BEC

EX 3A AND EX 3 B/C

To find vertically opposite angles we

look for angles in an X shape

Corresponding angles

A

BC

D E

FAngles ABC and ADE are

CORRESPONDING ANGLES

They are in the same position and they are equal

BC and DE are parallel lines

P

Q

R

T

S

An angle corresponding to <PQR is <TRS

x

x

1

2

34

5

67

8

An angle corresponding to

1 is

2 is

6 is

5 is

5

3

4

7Ex4a 1-4

This grid is made up two sets of parallel lines

>>>

>>>> >

>

>

>

The red shape between the lines is a parallelogram

The parm can slide along and down the grid

All the parallelograms in the grid are

All the blue angles in the same position and are equal

CONGRUENT

Equal angles in the same position are called

CORRESPONDING ANGLES

Find all the angles corresponding to the blue angle

To find corresponding angles we look for F

shapes

x

x

x

Copy the diagrams.Mark the angles which are corresponding to the given ones with an x

x

Ex4a 9 –11 ex 4b/c

Alternate anglesA

BC

D E

FAngles CBG and BGD are

ALTERNATE ANGLES

They are on opposite sides of the transverse line AF found between the parallel lines

BC and DE are parallel linesG

c =100º

a

b

a= a is vertically opposite c

b= b is corresponding to a

b is alternate to c b = c

ALTERNATE ANGLES ARE EQUAL

= 100 º

100 º

100 º

Q

R

T

S

An angle alternate to <PQR is <QRT

x

x

1

2

34

5

67

8

An angle ALTERNATE to

7 is

3 is

6

8

Ex5a 1-6

p

To find ALTERNATE angles we look for Z

shapes

x

x

x

x

Copy the diagrams Mark the angles which are alternate to the given ones with an x

Ex 5A 7-12 Ex 5B/C