1. Angle Relationships
Section 1-5

2. Adjacent angles are angles that: C) Have no interior points in common
Definition of
Adjacent
Angles
Adjacent angles are angles that:
A) Share a common side
B) Have the same vertex
C) Have no interior points in common

3. Determine whether 1 and 2 are adjacent angles.
No: They have a common vertex B, but
_____________ 1 2 B
no common side
Yes have the same vertex G and a common side with no interior points in common. 1 2 G N 1 2 J L
No: They do not have a common vertex or ____________
a common side

4. Complementary Angles Definition of Complementary Angles E A D 60° 30°
60° D E F
30° A B C

5. ABC is the complement of DEF and DEF is the complement of ABC.
Complementary Angles
If two angles are complementary, each angle is a complement of the other.
ABC is the complement of DEF and DEF is the complement of ABC.
60° D E F
30° A B C
Complementary angles DO NOT need to have a common side or even the same vertex.

6. Some examples of complementary angles are shown below.
75° I
15° H
50° H
40° Q P S
30°
60° T U V W Z

8. Supplementary Angles Definition of Supplementary Angles D C 130° 50° B
130° D E F
50° A B C

9. Supplementary angles add up to 180º.
40º
120º
60º
140º
Adjacent and Supplementary Angles
Supplementary Angles but not Adjacent

10.  I is the supplement of  H and  H is the supplement of  I.
Supplementary Angles
If two angles are supplementary, each angle is a supplement of the other.
 I is the supplement of  H and  H is the supplement of  I.
75° I
105° H
Supplementary angles DO NOT need to have a common side or even the same vertex.

11. Some examples of supplementary angles are shown below.
105° H
75° I
50° H
130° Q P S
60°
120° T U V W Z
and

12. Linear Pairs of Angles
Definition of
Linear Pairs
Two angles form a linear pair if and only if (iff):
A) They are adjacent
B) Their non-common sides are opposite rays C A D B 1 2
A Linear Pair is a set of Supplementary/Adjacent Angles

13. Linear Pairs of Angles In the figure, and are opposite rays.1 2 M 4 3 E H T A C
1) Name the angle that forms a
linear pair with 1.
ACE
ACE and 1 have a common side
the same vertex C, and opposite rays
and
2) Do 3 and TCM form a linear pair? Justify your answer.
No. Their noncommon sides are not opposite rays.

14. Two angles are vertical iff :
Vertical Angles
Definition of
Vertical
Angles
Two angles are vertical iff :
they are two non-adjacent angles formed by a pair of
intersecting lines.
Vertical angles:
1 and 3 1 4 2
2 and 4 3

15. Vertical Angles Vertical angles are congruent. Theorem: Vertical Angle2
1  3 3 1
2  4 4

16. Vertical Angles Find the value of x in the figure: (x – 10) = 125.
125°
x = 135.

17. Supplementary angles B C G A D F E

18. Complementary angles E F D C G J H

19. Perpendicular lines special intersecting lines that form right angles
Perpendicular lines intersect to form 4 right angles.

20. Congruent Angles Definition of Congruent
Two angles are congruent iff, they have the same
______________.
degree measure
B  V iff
50° V
mB = mV
50° B

21. HOMEWORK Pg
#1-26, 29-32
36-41