1-5 Angle Relationships
What are:
adjacent angles
linear pairs
vertical angles
complementary angles supplementary angles
perpendicular lines
Adjacent angles are two angles that lie in the same plane and have a common vertex and a common side, but no common interior points.
Adjacent angles
12
Linear Pair
A linear pair is a pair of adjacent angles with noncommon sides that are opposite rays.
1 2
Definition
Two angles, , form a linear pair if and only if A, B, and C are collinear and D is not on .
DBCABD and
AC
A B C
D
Name all the linear pairs
FKGandJKF GKHandFKG
HKJandGKH
F
G
H
K
J
JKFandHKJ
Vertical Angles
OR…When two lines intersect, they form two pairs of vertical angles.
Two angles are vertical angles if and only if their sides form two pairs of opposite rays.
1
2
3
4
Definition
Complementary angles are two angles whose measures add up to 90°
90ABDCBDABC
A
B
C
D
Try itFind the measures of
461m
1
2
3
134°
1342m 463m
.3,2,1
Definition
Supplementary angles are two angles whose measures add up to 180°
180TSURST
R S
T
U
Linear Pair Postulate
The angles in a linear pair are supplementary
What is the difference?
Supplementary because it adds to 180°
Supplementary because it adds to 180°
Linear pair because both angles are on the same line.
AND
Complementary or Supplementary?
Angles can be complementary or supplementary regardless of their location.
PR toarycomplementis
P R
41° 49°41° 139°
P S
PS toarysupplementis
64If Xm find the measures of the angles that are complementary and supplementary to X
Complementary
90°− 64° = 26°
Supplementary
180°− 64° = 116°
Review
p. 46
Review
p. 47
Assignment 1-5
Page 51, 8-17, 19-21
Angle Relationships Day 2
What are perpendicular lines?
What can be assumed or not assumed in a drawing?
Perpendicular Lines
Lines, line segments or rays that form right angles are perpendicular.
A B
CD
Perpendicular Lines A
B
CD
Perpendicular lines intersect to form four right angles.Perpendicular lines intersect to form congruent adjacent angles.Segments and rays can be perpendicular to lines or other line segments and rays.The right angle symbol in the figure indicated that the lines are perpendicular.
To Assume or Not to Assume…
In the figure, do you think you would be justified in assuming that:
B, C, and E are collinear?
?FCEACB BE ll GD?
D
A
BC
E
F
G
Make a List…
Make a list of rules about what you think you can and cannot assume.
A
BC
E
F
G
What can and cannot be assumedYou May Assume: You May Not Assume
(unless marked):Things that look straight are straight. Exact measurements
and relative sizes of figures.
Points shown on a line are collinear.
All points shown are coplanar.
Parallel or perpendicular lines.
Relative position of points are accurate (intersection, between-ness).
Congruence
To Assume or Not to Assume…Point S is between R
and T.Points R,S, and T are
collinear.
Point S is the midpoint of RT.
VY<TY
STRS
ZWVR .anglerightaisZYV
R S TV
W
Y
Z
Assignment 1-5 Day 2
Worksheet 1-5
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