SPECIAL SPECIAL PAIRS OF PAIRS OF ANGLESANGLES

Congruent AnglesCongruent Angles: : Two angles that Two angles that

havehave equal equal measures.measures.

Congruent Congruent AnglesAngles

32

32,m A m B

so A B

A

B

Angle BisectorAngle Bisector: a : a ray that divides an ray that divides an angle into 2 angle into 2 congruent angles.congruent angles.

Angle BisectorAngle Bisector

21

1 2 B

C

Suppose bisectsSuppose bisects

andand

Find: Find: 70m ABD

B

C

A

D

BC��������������

ABD

m CBD35

Suppose bisectsSuppose bisects

andand

Find: Find: 25m CBD

B

C

A

D

BC��������������

ABD

m ABC25

Adjacent AnglesAdjacent Angles: two : two coplanar angles that coplanar angles that share a common vertex share a common vertex and side, but have no and side, but have no interior points in interior points in common.common.

Adjacent Adjacent AnglesAngles

21

Nonadjacent Nonadjacent AnglesAngles

21

1

2

Linear PairLinear Pair: A pair of : A pair of adjacent angles adjacent angles whose non-common whose non-common sides are opposite sides are opposite rays.rays.

Linear PairLinear Pair

1 2

How many Linear How many Linear pairs can you name?pairs can you name?

14 23

1 2

2 3

3 4

4 1

Vertical AnglesVertical Angles: : Two non-adjacent Two non-adjacent angles formed angles formed when 2 lines when 2 lines intersectintersect

Vertical Vertical AnglesAngles

1 2

Also Vertical Also Vertical AnglesAngles

1

2

m ABC m CBD m ABD

The Angle Addition The Angle Addition PostulatePostulate: If C is a point : If C is a point in the interior of in the interior of then:then:

ABD

m ABC m CBD m ABD

B

C

A

D

For adjacent angles

______ ________ _______

m DAB m BAC m DAC

B

CA

D

______ ________ _______

m CBD m DBA m CBA

B

C

A

D

______ ________ _______

Supplementary Supplementary AnglesAngles: Two : Two angles whose angles whose measures total 180measures total 180

Supplementary Supplementary AnglesAngles

122 58

180m A m B A B

Suppose two angles are Suppose two angles are supplementary. If one supplementary. If one angle is 30 degrees, angle is 30 degrees, what is the measure of what is the measure of its supplement?its supplement?

150

Suppose two angles are Suppose two angles are congruent and congruent and supplementary. What supplementary. What are their measures?are their measures?

90

Suppose two angles are Suppose two angles are supplementary. If one supplementary. If one angle is angle is xx degrees, what degrees, what is the measure of its is the measure of its supplement?supplement?

180 x

Complementary Complementary AnglesAngles: Two : Two angles whose angles whose measures total 90measures total 90

Complementary Complementary AnglesAngles 32

58A

B90m A m B

Suppose two angles are Suppose two angles are complementary. If one complementary. If one angle is 30 degrees, angle is 30 degrees, what is the measure of what is the measure of its complement?its complement?

60

Suppose two angles are Suppose two angles are congruent and congruent and complementary. What complementary. What are their measures?are their measures?

45

Suppose two angles are Suppose two angles are complementary. If one complementary. If one angle is angle is xx degrees, what degrees, what is the measure of its is the measure of its complement?complement?

90 x

Perpendicular Perpendicular LinesLines: Two lines : Two lines that intersect to that intersect to form right angles.form right angles.

Perpendicular lines form Perpendicular lines form 4 right angles:4 right angles:

l

m

Perpendicular Perpendicular Lines:Lines:

l m l

m

Perpendicular lines form Perpendicular lines form 4 right angles:4 right angles:

l

m

But you only need 1 right But you only need 1 right angle to know they are angle to know they are Perpendicular Lines: Perpendicular Lines:

lm

Let’s see Let’s see what you what you recall…recall…

Linear PairLinear Pair1

2

Adjacent Adjacent AnglesAngles

21

Vertical Vertical AnglesAngles

1 2

Angle BisectorAngle Bisector

21

1 2 B

C

m CBA m ABD m CBD

B

C

A

D

______ ________ _______

Congruent Congruent AnglesAngles

32

32A B

A

B

Supplementary Supplementary AnglesAngles

122 58

180m A m B A B

Now Go Now Go Practice!Practice!

The EndThe End