Transcript Complementary angles

1-5 Angle Relationships
What are:
adjacent angles
linear pairs
vertical angles
complementary angles
supplementary angles
perpendicular lines
Adjacent angles
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.
1
2
Linear Pair
A linear pair is a pair of adjacent angles
with noncommon sides that are opposite
rays.
1
2
Definition
Two angles, ABD and DBC, form a
linear pair if and only if A, B, and C
are collinear and D is not on AC .
D
A
B
C
Name all the linear pairs
JKF and FKG
FKG and GKH
F
G
K
H
J
HKJ and JKF
GKH and HKJ
Vertical Angles
Two angles are vertical angles if and only if
their sides form two pairs of opposite rays.
OR…When two lines intersect, they form
two pairs of vertical angles.
2
1
3
4
Definition
Complementary angles are two angles
whose measures add up to 90°
A
C
B
D
ABC  CBD  ABD  90
Try it
Find the measures of 1, 2, 3.
2
1
3
134°
m1  46
m3  46
m2  134
Definition
Supplementary angles are two
angles whose measures add up
to 180°
T
R
S
U
RST  TSU  180
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°
AND
Linear pair because
both angles are on the
same line.
Complementary or Supplementary?
41°
49°
P
R
41°
139°
P
S
R is complement ary to P S is supplement ary to P
Angles can be complementary or supplementary
regardless of their location.
If mX  64 find the measures of the
angles that are complementary and
supplementary to X
Complementary
Supplementary
90°− 64° = 26°
180°− 64° = 116°
Review
Review
Assignment 1-5
Page 51, 8-17,
25-28
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.
B
A
D
C
B
Perpendicular Lines
A
C
D
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?
ACB  FCE ?
F
A
B
E
C
BE ll GD?
G
D
Make a List…
Make a list of rules
about what you think
you can and cannot
assume.
F
A
B
E
C
G
What can and cannot be assumed
You May Assume:
Things that look
straight are straight.
You May Not Assume
(unless marked):
Points shown on a line
are collinear.
Exact measurements
and relative sizes of
figures.
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.
RS  ST
Point S is the midpoint
of RT.
VR  ZW
ZYV is a right angle.
VY<TY
Z
V
Y
W
R
S
T
Assignment 1-5 Day 2
p. 52, 36-41
And worksheet 1-5