example 1.name all angles with b as a vertex. 2. name the sides of angle 5. 3. write another name...

Example

1.Name all angles with B as a vertex.

2. Name the sides of angle 5.

3. Write another name for angle 6.

Example

Classify each angle as right, obtuse, acute or straight.1. Angle TYV2. Angle WYT3. Angle TYU4. angleTYX

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. A pair of angles whose sides form opposite rays.

Definition:

4

3

2

1A

Q

D

B

C

Examples:

2 and 4

1 and 3

Vertical Angles Cont.

Non – Example:

Remember: To form a vertical pair you have to have two intersection lines.

Linear Pair

Definition: Is a pair of adjacent angles who’s non-common sides are opposite rays.

Example:

Non-example:

EX 1: 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

Example 2Find the value of x and the measure of each

angle

(3x+6)°

(x-4)°

Example 3-The measure of two complimentary angles are 16z-9 and 4z+3. Find the measures of the two angles.

Lesson 1-5: Pairs of Angles 12

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°

Example 4Find the value of x and the measure of

each angle

(3x-1)°(2x+6)°

Perpendicular Lines

Definitions: Lines that form two right angles.

Symbolized By :

Example 6

YWXZ

X

Z

W

Y

Example 7:Find x and y so that are

Perpendicular ADandBE