1. Chapter 1 Section 6 Angles
Geometry
Chapter 1 Section 6
Angles

2. 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

3. The Ray A B
Is called Ray BA never Ray AB

4. Name The Ray R G

5. Angle 2 rays with a common endpoint
The common endpoint is called the Vertex
The rays are called Sides
Side
Vertex
Side

6. Name an angle G T B L G L TGB L 1 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

7. Interior and exterior of an angle

8. 3 Letter Angle Name
A 3 letter angle name must be used if more than one angle shares a vertex T R F S
If you named an angle L R
Would you refer to L TRF , L TRS or L SRF?

9. 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
L BTG B G T V C Z E

10. To Read an angle name L BTZ L BTG L CVE L EVT L ZTV L GTV L BTV L ZTG

11. 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

12. 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

13. Angle Congruence
If 2 angles have the same measure then they are congruent
If L L R then
m L Q = m L R Q R

14. Angle Addition Postulate
If R is on the interior of angle PQS Then m L PQR + m L RQS = m L PQS P Q R S

15. Angle Addition Postulate
L GFE = 3x + 7
L DFG = 4x + 20
L EFD = 5x + 3
find x
find L DFG G F E D

16. Classifying Angles 00 < angle < 900 Acute
Degree Measure
Classification
00 < angle < 900
Acute
900 < angle < 1800
Obtuse
angle = 900
Right
angle = 1800
Straight

17. Restrictions on an Angle
If L NHM is Obtuse then
900 < L NHM < 1800
If L KJW is Acute then
00 < L NHM < 900

18. 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 < 176
43 < x < 88

19. Restrictions on an Angle
If L DRW is Obtuse and L DRW = 3x + 9 find the restrictions on x ___0 < L DRW < ___0

20. Angle Bisector If L GFE @ L EFD then FE is an angle bisector of L GFD
An Angle Bisector is a Ray that divides an angle into angles G
If L L EFD then
FE is an angle bisector
of L GFD F E D

21. If FE is an angle bisector of L GFD and
L GFD = 5x -3
L GFD = 2x +12
Find L EFD G F E D

22. Do Now
Page
Problems
10 – 12
17 – 28
33 – 39