angle relationship sec 1.5 sol: g.4c,d adjacent angles definition: 2 angles that lie on the same...
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Angle Relationship
Sec 1.5Sol: G.4c,d
Adjacent Angles
Definition: 2 angles that lie on the same plane, have a common vertex and a common side, but have no common interior points.
Example: Non – Example:
BA
D
CA
C
D
B
CBDABCand BCDABCand
No Common Vertex
Lesson 1-5: Pairs of Angles
Vertical Angles
2 non-adjacent angles formed by two intersecting lines. Opposite angles are congruent.
Definition:
4
3
2
1A
Q
D
B
C
Examples:
1 and 3
2 and 4
Vertical Angles Cont.
Non – Example:
Remember: To form a vertical pair you have to have two intersection lines.
Linear PairDefinition: Is a pair of adjacent angles who’s
non-common sides are opposite rays.Example:
Non-example:
A
B D C
BDA and CDA are a linear pair
EX: Identify angle pairs
4 532
1
1. Identify the vertical pairs.
2. Identify all the linear pairs.
3. Identify the Adjacent angles.
Lesson 1-5: Pairs of Angles 9
Complementary Angles
A pair of angles whose sum is 90˚Definition:
Examples:
21
Q
AB
C 1
2
Q
R
AB
F
GEven when two angles are non adjacent they can beAdded together to form a 90 degree angles
m1 = 40°m2 = 50°
9021 mm
Lesson 1-5: Pairs of Angles 10
Supplementary Angles
A pair of angles whose sum is 180˚Definition:
Examples:
Adjacent supplementary angles are also called “Linear Pair.”
Non-Adjacent Angles
2 1
A Q
B
C
1
2
A QR
BF
Gm2 = 140°
m1 = 40°
Ex: Angle Measure
Find the measure of two Complimentary angle if m1 = 2x + 3 and m2 = 3x – 8.
Example
G J
H
I
K
(9x – 4)(4x + 7)
Suppose mGIJ = 9x – 4 and mJIH = 4x – 11. Find the value of x and mKIH.
If line RU and line ST intersect at V, what is the measure of ?
RVS
T
V
R
S U
(8x – 12) (5x + 3)
Perpendicular Lines
Definitions: Lines that form two right angles.
Symbolized By : Read “Perpendicular to”
X
Z
W
Y
YWXZ
Example:Find x and y so that are
Perpendicular ADandBE
Assignments
Classwork: WB Pg 21 1-3,6,7,9,11-16,18,26
Homework:Pg 37 1-10,16-23,25-27,29