Angle facts
P
R
^
PQR
and
^
RQS
Add up to 90 º
Two angles which make a RIGHT angle are
aº
COMPLEMENTARY
bº
Q
a º is the complement of b º
S
and b º is the complement of a º
aº +
bº
=
90 º
the complements of the following angles are
10 º
80 º
17 º
73 º
36 º
54 º
50 º
40 º
81 º
9º
57 º
33 º
55 º
45 º
35 º
45 º
84 º
6º
<ABD or
A
D
the complement of < DBC is <EBC
< EBC = 72 º the size of <DBC is
C
B
the size of <ABD is
E
P14 ex 1A q 1,2,4,5,7 ex 1B
72 º
18 º
Supplementary angles
H
<EFH and <HFG add up to 180 º
pº
E
Two angles which make a STRAIGHT angle
are
qº
G
F
SUPPLEMENTARY
a º is the supplement of b º
and b º is supplement of a º
pº +
qº
=
180 º
the supplements of the following angles are
60 º
120 º
130 º
50 º
5º
175 º
100 º
80 º
168 º
12 º
55 º
125 º
178 º
2º
45 º
135 º
90 º
90 º
A
E
D
B
C
The supplement of <AED is
<ABC
The supplement of <CED is
<CEB
<AED IS140 º
<DEC is 75 º
<AEB is
<BEC is
P 16 EX 2A 1,2,5,6,7 AND EX 2B/C 1,2,3,4,
40 º
105 º
Vertically opposite angles
B
A
E
D
Vertically opposite
angles are found on
opposite sides of a
vertex
C
< AED IS VERTICALLY
OPPOSITE
<BEC
< AEB IS VERTICALLY
OPPOSITE <DEC
A
bº + aº = 180º
aº
D
cº
B
E
bº
bº + cº = 180º
aº must be equal to cº
C
<AEB and <DEC are vertically opposite angles
vertically opposite angles are equal
Another pair of vertically
opposite angles are
<AED and
EX 3A AND
EX 3 B/C
<BEC
To find vertically opposite angles we
look for angles in an X shape
Corresponding angles
A
C
B
D
E
BC and DE are
parallel lines
Angles ABC and ADE are
F
CORRESPONDING ANGLES
They are in the same position and they
are equal
P
An angle corresponding to
<PQR is
<TRS
Q
T
x
R
x
An angle corresponding to
S
4
3
6
2
7
8
1
5
Ex4a 1-4
1 is
5
2 is
3
6 is
4
5 is
7
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
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
To find corresponding
angles we look for F
shapes
Copy the diagrams.Mark the angles which are
corresponding to the given ones with an x
x
x
x
x
Ex4a 9 –11 ex
4b/c
Alternate angles
A
C
B
D
G
E
BC and DE are
parallel lines
Angles CBG and BGD
F
ALTERNATE
are
ANGLES
They are on opposite sides of the transverse line
AF found between the parallel lines
a
c =100º
b
b is alternate to c
= 100 º
a=
100 º
b=
100 º
b
a is vertically
opposite c
b is corresponding to
a
= c
ALTERNATE ANGLES ARE EQUAL
p
An angle alternate to
<PQR is
<QRT
Q
x
x
R
An angle ALTERNATE to
T
S
4
3
6
2
7
8
1
5
Ex5a 1-6
7 is
6
3 is
8
To find ALTERNATE
angles we look for Z
shapes
Copy the diagrams Mark the angles which are
alternate to the given ones with an x
x
x
x
Ex 5A 7-12 Ex 5B/C
x