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