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Warm-Up: Billiards (“Pool”)PowerPoint Presentation

Warm-Up: Billiards (“Pool”)

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### 1.4 Angles & their Measures

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

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:

- 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 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 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 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

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 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 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: 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: 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

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 AnglesExample 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

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 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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