Angle Relationships

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Angle Relationships
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• Line a never ending straight path of points
• How to name lines
• Use lowercase italic letter
• h
• By naming two points on the line and use line
  symbol (points are labeled by capital
  letters)

A B
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Ray a part of a line that has one endpoint and
extends indefinitely in one direction How to
name rays By the endpoint and one point on the
ray
C
B
D
A
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• How to name angles
• By the vertex
• Point, vertex, point

1
A
C
B
A
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Parallel lines two lines in the same plane
equidistant that do not intersect (symbol
a ll b ) Transversal a line that intersects
two parallel lines to form angles
a
b
a
b
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Acute angle measure is more than 0 degrees and
less than 90 degrees Right angle measure is
exactly 90 degrees Obtuse angle measure is more
than 90 degrees and less than 180
degrees Straight angle measure is 180 degrees
a line
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Adjacent angles angles that are side by side and
share a ray
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Special Adjacent Angles Complementary angles
angles that when added together equal 90
degrees Supplementary angles angles that
when added together equal 180 degrees
55o
x
x
59o
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Find the missing angle measurements.
xo
78o
137o
xo
62o
xo
180 137 43o
90 62 28o
90 78 12o
xo
43o
54o
xo
33o
180 54 43 83o
180 33 147o
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Perpendicular angles adjacent 90 degree
angles (symbol )
b
C
c
D
A
G
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Congruent same shape same angle measurements
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Alternate Interior Angles Non adjacent
interior angles found on opposite sides of the
transversal measures are congruent Examples
line a ll b and cut by transversal c
c
a
c
b
a
a
c
b
b
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Alternate Exterior Angles Non adjacent
exterior angles found on opposite sides of the
transversal measures are congruent Examples
line a ll b and cut by transversal c
c
a
c
b
a
a
c
b
b
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Corresponding Angles Non adjacent angles found
on the same side of the transversal in the same
position on the parallel lines measures are
congruent
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Examples line a ll b and cut by transversal c
c
c
a
a
b
b
c
c
a
a
b
b
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Vertical angles angles that are opposite each
other and share a vertex angle measures are
congruent
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Let's Put It All Together Now!!!
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Line a ll b and cut by transversal c
Why is Why is
Why is Why is Why is Why is Why is Why
is Why is Why is
Vertical Corresponding Alt interior Alt
exterior Corresponding Alt exterior Vertical Corre
sponding Corresponding Alt interior
1
2
3
4
5
6
7
8
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Line a ll b and cut by transversal c. Find the
measurements of all of the angles.
1
2
3
4
5
6
7
8
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Line f ll g and cut by transversals w and r. Find
the measurements of all the other angles.
78o 34o 68o 68o 78o 112o
68o 78o 102o 102o 112o 68o
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1
3
f
4
6
5
9
10
g
7
8
11
12
13
14
w
r