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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 Measures. Objectives: Define: Angle, side, vertex, measure, degree, congruent

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Warm up billiards pool
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 measures

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


Angle symbol
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)


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
Example 1: Naming Angles ones and a larger one). therefore, none of them should be called <B. The vertex is ALWAYS in the middle of the name

One angle only:

< EFG or < GFE

Three angles:

< ABC or < CBA

< CBD or < DBC

< ABD or < DBA


Angle measurement
Angle Measurement ones and a larger one). therefore, none of them should be called <B. The vertex is ALWAYS in the middle of the name


Postulate 3 protractor post
Postulate 3 ones and a larger one). therefore, none of them should be called <B. The vertex is ALWAYS in the middle of the name: 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 ___________ ones and a larger one). therefore, none of them should be called <B. The vertex is ALWAYS in the middle of the name

C is ___________

D is ___________

Interior or Exterior?

in the interior

in the exterior

on the <

B

C

D

A


Adjacent angles
Adjacent Angles ones and a larger one). therefore, none of them should be called <B. The vertex is ALWAYS in the middle of the name

  • 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


Postulate 4 angle addition postulate
Postulate 4:Angle Addition Postulate ones and a larger one). therefore, none of them should be called <B. The vertex is ALWAYS in the middle of the name


Example 2
Example 2: ones and a larger one). therefore, none of them should be called <B. The vertex is ALWAYS in the middle of the name

m < FJH = m < FJG + m < GJH

m < FJH = 35° + 60°


Example 3
Example 3: ones and a larger one). therefore, none of them should be called <B. The vertex is ALWAYS in the middle of the name

.

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


Types of angles

Acute angle – ones and a larger one). therefore, none of them should be called <B. The vertex is ALWAYS in the middle of the name

Right angle –

Obtuse angle –

Straight angle –

Measures between 0o & 90o

Measures exactly 90o

Measures between 90o & 180o

Measures exactly 180o

Types of Angles


Example 4 classifying angles
Example 4: ones and a larger one). therefore, none of them should be called <B. The vertex is ALWAYS in the middle of the nameClassifying Angles

  • A. straight

  • B. acute

  • C. obtuse


Example 5

Name an acute angle ones and a larger one). therefore, none of them should be called <B. The vertex is ALWAYS in the middle of the name

<3, <2, <SBT, or <TBC

Name an obtuse angle

<ABT

Name a right angle

<1, <ABS, or <SBC

Name a straight angle

<ABC

Example 5:

S

T

3

1

2

A

B

C


Assignment general 1 4 a honors 1 4 b
Assignment ones and a larger one). therefore, none of them should be called <B. The vertex is ALWAYS in the middle of the nameGeneral 1.4 AHonors 1.4 B


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