Angle Measure

Sec: 1.4Sol: G.4d,e

Ray

• Is Part of a line• Has one endpoint and extends indefinitely in

one direction.• Named by stating the endpoint and any other

point on the ray. (endpoint must be stated first.)

Denoted with an arrow pointing in one direction. AB

Example

Named:Or

Note: E has to go first!!!

EF

G

EF EG

Opposite Rays

• Two rays that fall on the same line, but go in opposite directions.

are opposite rays. They are also collinear rays.

Q P R

PRPQ,

Angles

• Are formed By two non-collinear rays.• They have a common endpoint.• The two rays are called sides of an angle.• The common endpoint is the vertex.

A

C

BVertex

Side

Side AB

AC

Lesson 1-4: Angles 7

There are three ways to name an angle

ABC or CBA

Using 3 points: The vertex must be the middle letter

This angle can be named as

Using 1 point: using only vertex letter (only used when there is only one angle present).

Since B is the vertex of only this angle, this can also be called .A

BC

B

Lesson 1-4: Angles 8

Naming an Angle - continued

Using a number: when naming with a number you use the number on the interior of the angle.

2

* The “1 letter” name is unacceptable when …more than one angle has the same vertex point. In this case, use the three letter name or a number if it is present.

2

A

B C

Angles Continued

• Name the following angle.

A

C

B

4,,, CABBACA

4

Lesson 1-4: Angles 10

Example

K

32

K

L

M

P

Therefore, there is NO in this diagram.There is , ,LKM PKM and LKP

2 3 5!!!There is also and but there is no

K is the vertex of more than one angle.

Lesson 1-4: Angles 11

Angle and Points

Angles can have points in the interior, in the exterior or on the angle.

Points A, B and C are on the angle. D is in the interior and E is in the exterior. B is the vertex.

A

BC

D

E

Example

1.Name all angles with B as a vertex.

2. Name the sides of <5.

3. Write another name for <6.

Classifying Angles:Right Angle Acute Angle Obtuse Angle Straight Angle

An angle whose measure is exactly 90°.

An angle whose measure is less than 90°

An angle whose measure is between 90° and 180°

An angle whose measure is exactly 180°

A B C

D

Example

Classify each angle as right, obtuse, acute or straight.1. <TYV2. < WYT3. <TYU4. <TYX

Congruent angles

• Two angles with the same angle measure(Note: Arcs on the angle signify that they are

congruent.)Example:

Lesson 1-4: Angles 16

Angle Addition Postulate

R

M K

W

The sum of the two smaller angles will always equal the measure of the larger angle.

Complete:

m ____ + m ____ = m _____MRK KRW MRW

Postulate:

Lesson 1-4: Angles 17

Adding Angles

22°

36°

21

D

B

C

A

Therefore, mADC = 58.

m1 + m2 = mADC also.

Lesson 1-4: Angles 18

Example: Angle Addition

R

M K

W

3x + x + 6 = 90 4x + 6 = 90 – 6 = –64x = 84x = 21

K is interior to MRW, m MRK = (3x), m KRW = (x + 6) and mMRW = 90º. Find mMRK.

3xx+6 Are we done?

mMRK = 3x = 3•21 = 63º

First, draw it!

Lesson 1-4: Angles 19

Example: Angle Addition

R

M K

W

K is interior to MRW, m MRK = (2x + 10), m KRW = (4x - 3) and mMRW = 145º. Find mMRK and m KRW.

2x + 10

4x - 3 How can you check this?

First, draw it!

Angle Bisectors

• Is a ray that divides an angle into two congruent halves.

• bisects RPS,m RPQ = 3x+6°and the m∠QPS =4x-8° .Find m RPS.m RPS = m RPQ + m QPS

PQ

Assignments

Classwork: Handout

Homework: Handout