1.4 ANGLES

The two rays are called the sides of the angle.

The common endpoint of the two rays is called the vertex of the angle

An angle is a geometric figure that consists of two rays that share a common endpoint.

B

A

C

L ABC or L CBA OR L B

Angle (ABC)

•Every angle is named by three letters. The middle letter is the name of the vertex. •Another way to name an angle is by the angle’s vertex.•Look at the top of p.17 for other ways we can name angles

Naming an Angle

B

A

C

D

This confusing…

• Can we use just the vertex to name these angles?

B

A

C

D

21

How many angles are there?

3

Angle Measurements• We measure the size of an angle using

degrees.

• We measure the size of an angle using a protractor

HOW DO WE USE A PROTRACTOR?

This angle measures 90 degrees. It is a right angle.

You use a protractor to measure angles.

Right AngleA right angle is an angle measuringexactly 90 degrees.

This angle is less than 90 degrees. It is called an acute angle.

Acute AngleAn acute angle is an angle measuring between 0 and 90 degrees.

“Ohhhh look at the a cute little angle that is…..”

Obtuse Angle

This angle is greater than 90 degrees. It is called an obtuse angle.

An obtuse angle is an angle measuringbetween 90 and 180 degrees.

Straight Angle

• A straight angle is 180 degrees.

A straight angleIs a straight _____?

GAME TIME!

• The object of the game is to be the first to raise your hand

and correctly name what type of angle you see.

• The correct answer will be on the following slide!!

• Good luck!

AcuteAngle

ObtuseAngle

RightAngle

StraightAngle

GREAT JOB!!

Protractor Postulate (pg.18)• Read it on your own

• It basically tells us that we can use our protractor to line up and measure the degrees of angles (just as we lined up the ruler to measure length)

• It also discusses absolute value, just like with the number line

Angle Addition Postulate

• If point B lies in the interior of AOC, – then m AOB + m BOC = m AOC.– What is the interior of an angle?

If AOC is a straight angle

and B is any point not on AC, then m AOB + m BOC = 180.

Why does it add up to 180?

Congruent Angles

• Angles that have equal measure

Adjacent Angles

Two angles in a plane that have..

1. a common vertex

2. and a common side but no common interior points.

Common Vertex

Common Side

No Common interior Points

DuplexCommon Roof

Common Wall

No Common Things

Duplex Adjacent Angles

Common Roof Common Vertex

Common Wall Common Side

No Common things inside my house

No Common Interior Points

Remote time

T – AdjacentF – Not adjacent

12

T – AdjacentF – Not adjacent

1

2

T – AdjacentF – Not adjacent

1

2

T – AdjacentF – Not adjacent

1

2

T – AdjacentF – Not adjacent

1

2

Bisector of a segment

• A line, segment, ray or plane that intersects the segment at its midpoint.

A

B

P

3

3

Something that is going to cut

directly through the midpoint

Bisector of an Angle

• The ray that divides the angle into two congruent adjacent angles (pg 19)

Name the two congruent angles

B

AX

C

BX bisects L ABC

Assumptions

• There are certain things that you can conclude from a diagram and others that you can’t.

Group ProblemA

E

D

C

B

What can you Assume?A

E

D

C

B

Be Careful

What you can Assume?

1. All points shown are coplanar

2. AB, BD, and BE intersect at B.

3. A, B, C are collinear

4. B is between A and C

5. ABC is a straight angle

6. D is in the interior of ABE

7. ABD and DBE are adjacent angles.

A

E

D

C

B

What you can’t Assume?

• AB BCABD DBECBE is a right angle

A

E

D

C

B

A

E

D

C

B

Marks are used to indicate conclusions about size in a diagram.

Tick marks – indicate

congruent segments

Arc marks – indicate

congruent angles

Indicates a 90 degree angle

Lessons Learned…

1. Don’t Assume !

2. Follow this rule: You can draw conclusions about position, but not about size.

3. Use markings to help you find out information about the diagram

Practice on the White Boards

A

B

E DC

2 3 4

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Name the vertex of 3

A

B

E DC

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Name the right angle

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B

E DC

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State another name for 1

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B

E DC

2 3 4

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State another name for 6

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B

E DC

2 3 4

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State another name for 3

A

B

E DC

2 3 4

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State another name for 4

A

B

E DC

2 3 4

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State another name for 7

A

B

E DC

2 3 4

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State another name for 2

A

B

E DC

2 3 4

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State another name for 5

A

B

E DC

2 3 4

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State another name for 9

A

B

E DC

2 3 4

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