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Angle facts. P. R. ^. ^. PQR. and. RQS. Add up to 90 º. Two angles which make a RIGHT angle are. a º. COMPLEMENTARY. b º. a º is the complement of b º. Q. S. and b º is the complement of a º. a º + b º = 90 º.

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Angle facts
Angle facts

P

R

^

^

PQR

and

RQS

Add up to 90 º

Two angles which make a RIGHT angle are

a º

COMPLEMENTARY

b º

a º is the complement of b º

Q

S

and b ºis the complement of a º

a º + b º = 90 º


Angle facts

the complements of the following angles are

73 º

80 º

54 º

10 º

17 º

36 º

9 º

33 º

40 º

81 º

57 º

50 º

84 º

35 º

45 º

6 º

55 º

45 º

<ABD or

<EBC

A

the complement of < DBC is

D

< EBC = 72 º the size of <DBC is

18 º

C

B

the size of <ABD is

72 º

E


Supplementary angles
Supplementary angles

H

<EFH and <HFG add up to 180 º

Two angles which make a STRAIGHT angle

p º

q º

are

G

E

F

SUPPLEMENTARY

a º is the supplement of b º

and b ºis supplement of a º

p º + q º = 180 º


Angle facts

the supplements of the following angles are

175 º

60 º 130 º 5 º

100 º 168 º 55 º

178 º 45 º 90 º

120 º

50 º

12 º

125 º

80 º

2 º

135 º

90 º

The supplement of <AED is

<ABC

A

The supplement of <CED is

<CEB

E

D

B

<AED IS140 º

<AEB is

40 º

<DEC is 75 º <BEC is

105 º

C


Vertically opposite angles
Vertically opposite angles

B

A

Vertically opposite angles are found on opposite sides of a vertex

E

< AEB IS VERTICALLY OPPOSITE

<DEC

D

C

< AED IS VERTICALLY OPPOSITE

<BEC


Angle facts

To find vertically opposite angles we look for angles in an X shape


Angle facts

A

bº + aº = 180º

B

E

bº + cº = 180º

D

aº must be equal to cº

C

<AEB and <DEC are vertically opposite angles

vertically opposite angles are equal

<AED and

<BEC

Another pair of vertically opposite angles are


Corresponding angles
Corresponding angles

A

C

B

D

E

BC and DE are parallel lines

Angles ABC and ADE are

CORRESPONDING ANGLES

F

They are in the same position and they are equal


Angle facts

P

An angle corresponding to <PQR is

<TRS

Q

T

x

R

x

An angle corresponding to

S

4

1 is

3

1

5

7

6

2 is

8

3

2

5

4

6 is

7

5 is

Ex4a 1-4


Angle facts

This grid is made up two sets of parallel lines

The red shape between the lines is a parallelogram

The parallelogram can slide along and down the grid

>

>

>

>

>

>

>

>

>

>

>


Angle facts

All the parallelograms in the grid are

CONGRUENT

All the blue angles in the same position and are equal

Equal angles in the same position are called

CORRESPONDING ANGLES

Find all the angles corresponding to the blue angle




Alternate angles
Alternate angles to the given ones with an

A

C

B

BC and DE are parallel lines

D

G

E

Angles CBG and BGD are

ALTERNATE ANGLES

F

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


Angle facts

a to the given ones with an

c =100º

b

= 100 º

a is vertically opposite c

100 º

a=

b is corresponding to a

100 º

b=

b is alternate to c

b = c

ALTERNATE ANGLES ARE EQUAL


Angle facts

p to the given ones with an

An angle alternate to <PQR is

<QRT

Q

x

x

R

An angle ALTERNATE to

T

S

4

7 is

3

1

6

7

6

3 is

8

8

2

5


Angle facts

To find ALTERNATE angles we look for to the given ones with anZ shapes