Angle Relationships

Adjacent Angles

• Adjacent Angles1. Are “next to” each other2. Share a common side

C D Cand D are adjacentK

J Jand K are not adjacent - they do not share a side

Vertical AnglesVertical Angles1. Are across from each other when two lines

intersect2. Are Congruent

1

42

3

There are two pairs of vertical angles:

1 3

2 4

and

and

What appears to be true about these two pairs of angles?

We show that by using “tick marks” over the arcs

Complementary AnglesComplementary Angles-Two angles whose sum is 90°

AB

Aand B are complementary

MN

If the measure of is 37°, what is m ?

M

N is 53°N

Angles M and N are complementary.

Supplementary AnglesSupplementary Angles-Two angles whose sum is 180°

A B

Aand B are supplementaryM

N If the measure of is 152°, what is m ?M

M is 28°

NAngles M and N are supplementary.

Perpendicular LinesTwo lines are perpendicular if they intersect at 90° angles

mn

m n

Are these two lines ? No

Parallel Lines

• Parallel Lines1. Do not intersect2. Lie in the same plane

km k m

Are these lines parallel?

No; they would intersect if they both continued

Transversal

A line that “cuts through” two or more other lines (usually the other two are parallel)

Which line is the transversal?

Corresponding AnglesWhen a transversal cuts through two parallel

lines, it creates 4 sets of corresponding angles.Corresponding angles are angles that are in the

same position when a transversal cuts two parallel lines.

1 2 3 4

5 6 7 8

If I could cut out a whole where this rectangle is, and move it down, each angle would line up with its corresponding angle exactly.Therefore, corresponding angles are congruent.

Skew Lines

Skew Lines1. Lines that do not intersect2. Do not lie in the same plane

Lines and are skewWX !!!!!!!!!!!!! !

UV !!!!!!!!!!!!! !

Lines and are not skew; they are parallel. They lie in the same plane.

XU !!!!!!!!!!!!! !

YV !!!!!!!!!!!!! !

Apply what you know

• Find the measures of the seven missing angles.

125°