Angle Relationship

Sec 1.5Sol: G.3 and G.11

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

QR

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.

Perpendicular Lines

Definitions: Lines that form two right angles.Can intersect to form 4 right anglesIntersect to form congruent adjacent angles.Segments and rays can be perpendicular to

lines or other segments and rays.When you see a right angle symbol it

represents perpendicular lines.Symbolized By : Read “Perpendicular to”

Example

YWXZ

X

Z

W

Y

Example:Find x and y so that are

Perpendicular ADandBE