special pairs of angles
DESCRIPTION
SPECIAL PAIRS OF ANGLES. Congruent Angles : Two angles that have equal measures. Congruent Angles. A. B. Angle Bisector : a ray that divides an angle into 2 congruent angles. Angle Bisector. C. B. Suppose bisects and Find:. A. C. B. D. Suppose bisects - PowerPoint PPT PresentationTRANSCRIPT
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
211 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
211
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 22 33 44 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
BC
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
211 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