1. Warm-Up: Billiards (“Pool”)
Who has played pool?
What’s a “bank shot”?
How do you know where to hit the ball on
the side?
It’s all in the angles!
Angles are the foundation of geometry

2. 1.4 Angles & their Measures
Objectives:
Define: Angle, side, vertex, measure, degree, congruent
Name angles with the vertex always in the middle
Measure angles with a protractor
Identify congruent angles
Classify angles as acute, right, obtuse, or straight
Add and subtract angle measures using the angle addition postulate

3. Angles can also be named by a #. (<5)
Angle symbol:
2 rays that share the same endpoint (or initial point)
Sides – the rays XY & XZ
Vertex – the common endpoint; X Y X 5 Z
Named <YXZ, <ZXY (vertex is always in the middle), or <X (if it’s the only <X in the diagram).
Angles can also be named by a #. (<5)

4. In the figure, there are three different <Q’s (two smaller ones and a larger one). therefore, none of them should be called <B. The vertex is ALWAYS in the middle of the name

5. Example 1: Naming Angles
One angle only:
Three angles:
< EFG or < GFE
< ABC or < CBA
< CBD or < DBC
< ABD or < DBA

6. Angle Measurement

7. Postulate 3: Protractor Post.
The rays of an angle can be matched up with real #s (from 1 to 180) on a protractor so that the measure of the < equals the absolute value of the difference of the 2 #s.
55o
20o
m<A =
= 35o

8. Interior or Exterior? B is ___________ C is ___________
D is ___________
in the interior
in the exterior
on the < B C D A

9. Adjacent Angles
2 angles that share a common vertex & side, but have no common interior parts.
(they have the same vertex, but don’t overlap) such as <1 & <2 2 1

10. Postulate 4:Angle Addition Postulate

11. Example 2:
m < FJH = m < FJG + m < GJH
m < FJH = 35° + 60°

12. Example 3: . If m<QRP=5xo, m<PRS=2xo, & m<QRS=84o, find x.
5x+2x=84
7x=84
x=12
m<QRP=60o m<PRS=24o S P Q R

13. Types of Angles Acute angle – Right angle – Obtuse angle –
Straight angle –
Measures between 0o & 90o
Measures exactly 90o
Measures between 90o & 180o
Measures exactly 180o

14. Example 4: Classifying Angles
A. straight
B. acute
C. obtuse

15. <3, <2, <SBT, or <TBC <1, <ABS, or <SBC
Example 5:
Name an acute angle
<3, <2, <SBT, or <TBC
Name an obtuse angle
<ABT
Name a right angle
<1, <ABS, or <SBC
Name a straight angle
<ABC S T 3 1 2 A B C

16. Assignment General 1.4 A Honors 1.4 B