Geometry

Chapter 1 Section 6Angles

Rays

• A Ray has one endpoint and goes forever in one direction

• A Ray is named with the endpoint and one point on the ray

The Ray

A

B

Is called Ray BA never Ray AB

Name The Ray

G

R

Angle• 2 rays with a

common endpoint

• The common endpoint is called the Vertex

• The rays are called Sides

Side

Side

Vertex

Name an angle

With the angle Sign L and:•The vertex•A Point on one side, the vertex and a point on the other•A number designator

• L G

• L TGB• L 1

TB

G1

Interior and exterior of an angle

ExteriorInterior

3 Letter Angle Name

• A 3 letter angle name must be used if more than one angle shares a vertex

S

R

T

F

If you named an angle L RWould you refer to L TRF , L TRS or L SRF?

To Read an angle name

• Pick the first letter is on a side, the middle letter is the vertex, and the third letter is on the other side

Z

GB

T C

E

V

L BTG

To Read an angle name

• L BTZ• L BTG• L CVE• L EVT• L ZTV• L GTV• L BTV• L ZTGZ

GB

T C

E

V

Angle Measurement

• Angles are measured in degrees• All Angles have measurements

between 0 and 1800

The restrictions on an angle are 00 ≤ any angle ≤ 1800

Special angles

• An angle of measure 00 is a ray• An Angle of measure 1800 is called a

Straight Angle• A Straight Angle is formed by

Opposite Rays• An angle with a measure of 900 is

called a Right Angle

Angle CongruenceIf 2 angles have the same measure then they are congruent

Q R

If L Q L R then m L Q m L R

Angle Addition Postulate

If R is on the interior of angle PQSThen m L PQR + m L RQS = m L PQS

S

Q

P

R

Angle Addition Postulate

D

F

G

E

• L GFE = 3x + 7• L DFG = 4x + 20• L EFD = 5x + 3 find x find L DFG

Classifying Angles

Degree Measure Classification

00 < angle < 900 Acute900 < angle < 1800 Obtuse

angle = 900 Rightangle = 1800 Straight

Restrictions on an Angle

• If L NHM is Obtuse then900 < L NHM < 1800

• If L KJW is Acute then00 < L NHM < 900

Restrictions on an Angle

• If L NHM is Obtuse and L NHM = 2x+4 then find the restrictions on x

900 < L NHM < 1800 90 < 2x+4 < 180

86 < 2x < 17643 < x < 88

Restrictions on an Angle

If L DRW is Obtuse and L DRW = 3x + 9 find the restrictions on x

___0 < L DRW < ___0

Angle Bisector

An Angle Bisector is a Ray that divides an angle into 2 angles

D

F

G

E

If L GFE L EFD then FE is an angle bisector

of L GFD

Angle Bisector

D

F

G

E

If FE is an angle bisector of L GFD and•L GFD = 5x -3•L GFD = 2x +12 Find L EFD

Do Now

Page 49 - 51Problems

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