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"For every action there is an equal and opposite reaction."

~Newton's 3 Law of Motion

"For every angle there is typically another angle that is related/dependant/adjoined to it in some way."

~Bloch (2013)

* Adjacent Angles:

Adjacent angles are two coplanar angles with a common side, a common vertex and no common interior points.

3

2

1

4

Adjacent Adjoining Next to Neighbors

* Vertical Angles

Vertical angles are two angles whose sides are opposite rays.

3

2

1

4

Vertical Across

* Complementary Angles

Complementary angles are angles whose measures have a sum of 90. Each angle is called the complement of the other.

A

43

47

1

2

B

C comes before S 90 comes before 180

* Supplementary Angles

Supplementary angles are two angles whose measures

have a sum of 180. Each angle is called the supplement of the other.

1

2

43

137

B

A

C comes before S 90 comes before 180

On your own

2

3

1. Two pairs of vertical angles

2. Two pairs of adjacent angles

3. Two pairs of complementary angles

4. A pair of supplementary angles.

1

4

6

5

What we can and can not assume

when looking at a diagram...

Things that we can assume:

* Angles are adjacent

* Angles are adjacent and supplementary

* Angles are vertical

Things we can not assume:

* Angles or segments are congruent

* An angle is a right angle

* Angles are complementary

A LINEAR PAIR is a pair of adjacent angles whose non common sides are opposite rays. A pair of a linear pair form a straight angle.

D

B

C

A

Postulate 1-9 "Linear Pair Postulate"

If two angles from a linear pair, then they are supplementary.

Find the measure of each angle. Does this figure make sense?

L

What do we know about this

figure? Where do we start?

(2x + 24)

(4x + 36)

P

J

K

KPL + LPJ = 180

(2x + 24) + (4x +36) = 180

6x + 60 = 180

6x = 120

x = 20

4(20) + 36 = LPJ

2(20) + 24 = KPL

116 = LPJ

64 =

KPL

A _____________ is a ray which divides an angle into two congruent angles. Its endpoint is at the angle _________.

VERTEX

After using the segment bisector,

we can mark both angles as congruent

Ray BD bisects ABC. ABD has a measure of 3x-3. DBC has a measure of 2x + 7. Draw a figure, then find x and the measusure of each angle.

ABD = DBC

ABD = 3x - 3

= 3(10) - 3

= 27

3x - 3 = 2x + 7

x = 10

DBC = 2x + 7

= 2(10) + 7

= 27

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