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Angles. Lesson 1-4. Angle and Points. An Angle is a figure formed by two rays with a common endpoint, called the vertex. ray. vertex. ray. Angles can have points in the interior, in the exterior or on the angle. A. E. D. B. C.

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angles
AnglesLesson 1-4

Lesson 1-4: Angles

angle and points
Angle and Points
  • An Angle is a figure formed by two rays with a common endpoint, called the vertex.

ray

vertex

ray

  • Angles can have points in the interior, in the exterior or on the angle.

A

E

D

B

C

Points A, B and C are on the angle. D is in the interior and E is in the exterior.

B is the vertex.

Lesson 1-4: Angles

naming an angle 1 using 3 points 2 using 1 point 3 using a number next slide
Naming an angle:(1) Using 3 points (2) Using 1 point (3) Using a number – next slide

Using 3 points:

vertex must be the middle letter

This angle can be named as

Using 1 point:

using only vertex letter

*Use this method is permitted when the vertex point is the vertex of one and only one angle.

Since B is the vertex of only this angle, this can also be called .

A

C

B

Lesson 1-4: Angles

naming an angle continued
Naming an Angle - continued

Using a number:

A number (without a degree symbol) may be used as the label or name of the angle. This number is placed in the interior of the angle near its vertex. The angle to the left can be named

as .

A

B

2

C

* The “1 letter” name is unacceptable when …

more than one angle has the same vertex point. In this case, use the three letter name or a number if it is present.

Lesson 1-4: Angles

example
Example
  • K is the vertex of more than one angle.

Therefore, there is NO in this diagram.

There is

Lesson 1-4: Angles

5 types of angles
5 Types of Angles

Acute Angle:

an angle whose measure is less than 90.

Right Angle:

an angle whose measure is exactly 90 .

Obtuse Angle:

an angle whose measure is between

90 and 180.

Straight Angle:

an angle that is exactly 180 .

Reflex Angle:

an angle whose measure is greater than 180.

Lesson 1-4: Angles

measuring angles
Measuring Angles
  • Just as we can measure segments, we can also measure angles.
  • We use units called degrees to measure angles.
    • A circle measures _____
    • A (semi) half-circle measures _____
    • A quarter-circle measures _____
    • One degree is the angle measure of 1/360th of a circle.

360º

?

180º

?

?

90º

Lesson 1-4: Angles

adding angles
Adding Angles
  • When you want to add angles, use the notation m1, meaning the measure of 1.
  • If you add m1 + m2, what is your result?

m1 + m2 = 58.

m1 + m2 = mADC also.

Therefore, mADC = 58.

Lesson 1-4: Angles

angle addition postulate
Angle Addition Postulate

Postulate:

The sum of the two smaller angles will always equal the measure of the larger angle.

Complete:

m  ____ + m ____ = m  _____

MRK

KRW

MRW

Lesson 1-4: Angles

example angle addition
Example: Angle Addition

K is interior to MRW, m  MRK = (3x), m KRW = (x + 6) and mMRW = 90º. Find mMRK.

First, draw it!

3x + x + 6 = 90

4x + 6 = 90

– 6 = –6

4x = 84

x = 21

3x

x+6

Are we done?

mMRK = 3x = 3•21 = 63º

Lesson 1-4: Angles

angle bisector
Angle Bisector

An angle bisector is a ray in the interior of an angle that splits the angle into two congruent angles.

Example:

Since 4   6, is an angle bisector.

5

3

Lesson 1-4: Angles

congruent angles
Congruent Angles

Definition:

If two angles have the same measure, then they are congruent.

Congruent angles are marked with the same number of “arcs”.

The symbol for congruence is 

3

5

Example:

3   5.

Lesson 1-4: Angles

class work
Class work
  • Pg. 29 # 6, 21, 22, 25, 26
  • Pg. 30 # 33 to 38, 40, 42

Lesson 1-4: Angles