Download 2.5 Proving Angles Congruent

2.5 Proving
Angles Congruent
Vocabulary Terms
vertical angles—angles who's sides are opposite rays
1and
 2
1
3
4
3and4
2
Theorem 2.1—Vertical Angles Thm
vertical angles are congruent
1  2
3  4
Vocabulary Terms
adjacent angles—angles who have a common side
and a common vertex
**share a side
1
2
3
4
Vocabulary Terms
complementary angles— two angles who add up to 90º
A is a compliment
to B
1
2
50
A
40
B
supplementary angles—two angles
who add up to 180º
**make a straight line
Ex 1: Identify each type of
angle
a) Complementary
2,3
2
1
b) Vertical
5
3,5
c) Supplementary
4,5
4,3
3
4
Ex 2: What can you conclude
from the diagram?
3
4
5
1  2
1
2
Can I say…
3, 4 are adjacent
3  4 No
4, 5 are supplementary
2  5  180
2, 4
Yes
are vertical
Theorems
Theorem 2-2: Supplementary Thm
If 2 angles are supplements of the same angle (or congruent
angles),
then the 2 angles are congruent
1
1
2
3
2  3
**same for compliments
Theorems
Theorem 2-4: Right Angles
All right angles are congruent
Theorem 2-5:
If 2 angles are congruent and
supplementary, then each is a right
angle
Ex 3: Solve for variables
a)
2 y  3y  6
 y  6
y6
4x
2y
3y - 6
4 x  2  6   180
4 x  12  180
4 x  168
x  42
Ex 3: Solve for variables
b)
y
2x + 3
4x - 101
4 x 101  2 x  3
2 x  104
x  52
2  52   3  y  180
104  3  y  180
107  y  180
y  73
HW 2-5: WS 2-5