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PROVING
ANGLES
CONGRUENT
Vertical angles
Two angles whose sides form two pairs of opposite
rays
3
1
4
2
The opposite angles in vertical angles are congruent.
In this case angles 1 & 2 would be congruent
and angles 3 & 4 would be congruent.
Because angles 1 & 4 form a straight line as well as
angles 3 & 2 we only have to know the measure of
one angle to know all of the angle
600
200
1
3
2
4
600
1200
If angle 3 is 600, then angle 2 would be 1200 because
they make a straight angle of 1800. Then angle 4
would be 600 being vertical to angle 3 and angle 1
would be 1200 being vertical to angle 2
Adjacent angles
Two coplanar angles with a common side, a common
vertex, and no common interior points
In other words, two angles share one of the same
rays
Complementary angles
Two angles whose measures have the sum of 900
Each angle is called the complement of the other
400
500
As you can see from the figures the two angles can
be adjacent or they can be separated but the angles
must add up to 900
Supplementary angles
Two angles whose measures have the sum of 1800
Each angle is called the supplement of the other
Here again, they can be adjacent or they may be two
separate angles but their measure will be 1800
1050
750
Identifying Angle Pairs
Name a set of complementary angles
< 2 and < 3
A set of supplementary angles
< 4 and < 5
< 3 and < 4
Vertical angles
< 3 and < 5
2
1
5
3
4
F
A
E
B
C
Name the adjacent angles:
If m<EFD = 27, what is the m<AFD
180 – 27 = 153
D
F
A
E
B
C
D
Conclusions you can draw from the diagram
Adjacent angles
Adjacent supplementary angles
Vertical angles
Things you cannot assume
F
A
E
B
C
D
Angles or segments that are congruent
If an angle is a right angle
Lines are parallel or perpendicular
We can assume these if there are markings
What can you conclude
from this diagram?
<1 and <2 Congruent
<2 and <3 Adjacent
4
3
5
2
1
<4 and <5 adjacent
supplementary angles
<1 and <4 vertical angles
What conclusions can you
make here?
T
P
W
V
Q
Assignment
Page 100
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