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...
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Transcript of 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...
![Page 1: 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 angles which make a RIGHT angle are COMPLEMENTARY and b º is.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc85503460f94abdfd4/html5/thumbnails/1.jpg)
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
![Page 2: 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 angles which make a RIGHT angle are COMPLEMENTARY and b º is.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc85503460f94abdfd4/html5/thumbnails/2.jpg)
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
![Page 3: 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 angles which make a RIGHT angle are COMPLEMENTARY and b º is.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc85503460f94abdfd4/html5/thumbnails/3.jpg)
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
![Page 4: 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 angles which make a RIGHT angle are COMPLEMENTARY and b º is.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc85503460f94abdfd4/html5/thumbnails/4.jpg)
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,
![Page 5: 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 angles which make a RIGHT angle are COMPLEMENTARY and b º is.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc85503460f94abdfd4/html5/thumbnails/5.jpg)
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
![Page 6: 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 angles which make a RIGHT angle are COMPLEMENTARY and b º is.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc85503460f94abdfd4/html5/thumbnails/6.jpg)
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
![Page 7: 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 angles which make a RIGHT angle are COMPLEMENTARY and b º is.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc85503460f94abdfd4/html5/thumbnails/7.jpg)
To find vertically opposite angles we
look for angles in an X shape
![Page 8: 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 angles which make a RIGHT angle are COMPLEMENTARY and b º is.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc85503460f94abdfd4/html5/thumbnails/8.jpg)
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
![Page 9: 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 angles which make a RIGHT angle are COMPLEMENTARY and b º is.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc85503460f94abdfd4/html5/thumbnails/9.jpg)
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
![Page 10: 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 angles which make a RIGHT angle are COMPLEMENTARY and b º is.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc85503460f94abdfd4/html5/thumbnails/10.jpg)
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
![Page 11: 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 angles which make a RIGHT angle are COMPLEMENTARY and b º is.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc85503460f94abdfd4/html5/thumbnails/11.jpg)
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
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![Page 13: 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 angles which make a RIGHT angle are COMPLEMENTARY and b º is.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc85503460f94abdfd4/html5/thumbnails/13.jpg)
To find corresponding angles we look for F
shapes
![Page 14: 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 angles which make a RIGHT angle are COMPLEMENTARY and b º is.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc85503460f94abdfd4/html5/thumbnails/14.jpg)
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
![Page 15: 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 angles which make a RIGHT angle are COMPLEMENTARY and b º is.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc85503460f94abdfd4/html5/thumbnails/15.jpg)
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
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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
![Page 17: 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 angles which make a RIGHT angle are COMPLEMENTARY and b º is.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc85503460f94abdfd4/html5/thumbnails/17.jpg)
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
![Page 18: 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 angles which make a RIGHT angle are COMPLEMENTARY and b º is.](https://reader035.fdocuments.in/reader035/viewer/2022062516/56649dc85503460f94abdfd4/html5/thumbnails/18.jpg)
To find ALTERNATE angles we look for Z
shapes
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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