RayRay

An object that has one endpoint and continues

infinitely in ONE direction.

AngleAngle

An object that has two rays (called sides) with

a common endpoint (called the vertex).

Example 1

Name each of the following:

Sides:_____________________

Vertex:_________

Name:_____________________

A

B

C

Interior of an AngleInterior of an Angle

the space between the rays that create an

angle.

Exterior of an AngleExterior of an Angle

the space that is outside of the rays

Example 2

How does the diagram in EXAMPLE 1 differ from the diagram in this example?

Q

P

R

S

Example 3

A) Name a point in the interior of QPS in EXAMPLE 2.

B) Name a point in the exterior of QPR in EXAMPLE 2.

Q

P

R

S

AdjacentAdjacent

To be next to.

SHARING a side.

Angle Addition PostulateAngle Addition Postulate

The sum of two adjacent angles is equal to the

largest angle.

ANGLE ADDITION POSTULATE:

Q

P

R

S

If R is in the interior of QPS, then mQPR + mRPS = mQPS.

If mQPR + mRPS = mQPS, then R is in the interior of QPS.

ANGLE ADDITION POSTULATE:

Q

P

R

S

If R is in the interior of QPS, then mQPR + mRPS = mQPS.

If mQPR + mRPS = mQPS, then R is in the interior of QPS.

Example 4

If mPQS = 77 and mPQR = 32, then find mRQS.

P

Q

R

S

Example 5

If mAOC = 70, mAOB =(x + 10), and mBOC =x, find:

x = __________

mBOC = _______________

mAOB = _______________

O

A

B

C

Angles can be classified by their measure in degrees.

If an angle has a degree measure less than 90° it is classified as an _acute angle__.

If an angle has a degree measure equal to 90° it is classified as a __ right angle ____.

Acute AngleAcute Angle

An angle measuring

less than 90°

Right AngleRight Angle

An angle whose measure is exactly 90°

Obtuse AngleObtuse Angle

An angle measuring

greater than 90°

but less than 180°

Straight AngleStraight Angle

An angle measuring

exactly 180°

For each of the following anglesA) Name it.

B) Tell whether its measure is <90, >90, =90, or = 180. C) Classify it.

NAME:_________ OR ______MEASURE:________CLASSIFICATION___________

F

Y

I

NAME:_________ OR ______MEASURE:________CLASSIFICATION___________

T

L

C

NAME:_________ OR ______MEASURE:________CLASSIFICATION___________

T

R

S

NAME:_________ OR ______MEASURE:________CLASSIFICATION___________

N X S

35 125

CongruentCongruent

to be the same shape and same size.

Angle BisectorAngle Bisectora line, ray, or segment

that divides an angle into two congruent angles.

Example 7

If XZ is an angle bisector of WXY, name the two congruent angles that it forms.

WX

Z

Y

Example 8

FG bisects EFH. Find the value of x.

m EFG = (5x – 10); m GFH = (3x + 25)

I F H

EG

Example 9

FG bisects EFH. Find the value of x.

m GFH = (3x + 20); m EFH = (4x + 80)

I F H

EG