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.

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

1.4 Angles & their MeasuresObjectives:

•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

Angle symbol:

• 2 rays that share the same endpoint (or initial point)

Y

Z

X

Sides – the rays XY & XZ

Vertex – the common endpoint; X

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)

5

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

Example 1: Naming Angles

Angle MeasurementAngle Measurement

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 = 55-20

= 35o

Interior or Exterior?

• B is ___________• C is ___________• D is ___________

in the interior

in the exterioron the <

A

B

C

D

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

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Postulate 4:Angle Addition Postulate

Example 2:

m < FJH = m < FJG + m < GJHm < FJH = 35° + 60°

Example 3:.

Q

P S

R

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

Types of AnglesTypes of Angles• Acute angle –

• Right angle –

• Obtuse angle –

• Straight angle –

Measures between 0o & 90o

Measures exactly 90o

Measures between 90o & 180o

Measures exactly 180o

Example 4: Classifying Angles

• A. straight

• B. acute

• C. obtuse

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

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3

A B C

S

T

AssignmentGeneral 1.4 AGeneral 1.4 AHonors 1.4 BHonors 1.4 B