W

TY

R

E

Q

S

1. Name a plane.

2. Name a line.

3. Name a ray.

4. Name a point.

5. Name three collinear points.

6. Name four coplanar points.

7. Name a segment.

8. Do points T and Q lie on the same line?

9. Plane RYT plane EWTR is _______.

10. How many planes does point S lie on?

Homework Answerspg. 155)True6)False7)True8)True9)False10) True11) False12) True13) True14) False15) True16) False17) False18) True

pg. 1633) x = 634) x = 1135) x = 336) x = 737) y = 638) y = 739) z = 8

GE = 10, EH = 10 E is the midpoint of GH

40) z = 5 GE = 5, EH = 6 E is not the midpoint of

GH

In this section we will discuss the proper notation of angles, specific classifications of angles, and the properties of angle bisectors and the Angle Addition Postulate.

C

A

T

Angle – the figure formed by two rays that have the same endpoint.The two rays are

called the sides; the shared endpoint is called the vertex.

Vertex

Sides

We name an angle using three letters and the symbol.

Order Matters!! The vertex must be the letter in the middle!

C

A T

Acceptable:

CAT TAC

Unacceptable:

ACT TCA

Alternative Notation

C

TA

You can name an angle just with the vertex. This angle could be A.

Sometimes using only one letter may not be specific enough, because it may refer to more than one

angle. IF THERE IS ANY DOUBT,

USE THREE LETTERS!

B

CAB

CAT

BAT

We also may name angles with numbers.

C

T

B

A1

2

CAB is 1

BAT is 2

Measuring AnglesWe measure angles using a

protractor. The units for angle measurement is degrees.

Symbol for Degree:

Measure of Angle:

mABC

70°

Measure Angles #1-9 using your protractor.

Estimate to the nearest degree.

Classifying AnglesAcute Angle Obtuse Angle

Right Angle Straight Angle

A pair of opposite rays creates a straight angle.

An angle measuring between 0 and 90.

An angle measuring between 90 and 180.

An angle measuring exactly 90

An angle measuring exactly 180

Angle InteriorAny points that lie inside the angle.

A

B C

D

T

E

H

Congruent AnglesRecall the Definition of Congruent:

Figures that are the same shape and size.

Congruent Angles – angles that have equal measures.

MAT ZIP mMAT mZIP

Remember: Figures can be

congruent; measures can

be equal.

M

AT

Z

IP

120° 120°

Adjacent AnglesDefinition: two angles in a plane that have a common vertex and a common side but no common interior points.

C

T

B

A

CAB and BAT are adjacent angles.

CAT and BAT are NOT adjacent because they share interior points.

Angle BisectorDefinition: a ray that divides an angle into two congruent adjacent angles.

6060

XY

ZW

is an angle bisector.WY

XWYYWZ

Angle Addition Postulate

5065

AB

CO

If B lies on the interior of AOC, then mAOB + mBOC = mAOC.

mAOC = 115

B

QD

CmBQC = x - 7mCQD = 2x - 1

mBQD = 2x + 34

Find x, mBQC, mCQD, mBQD.

mBQC + mCQD = mBQD

3x – 8 = 2x + 34

x – 7 + 2x – 1 = 2x + 34

x – 8 = 34

x = 42

mBQC = 35

mCQD = 83

mBQD = 118

Update Postulate Section –

Angle Addition Postulate