Download GEOMETRY FACT 180 180 BAC CAD DAE abc ∠ +

Diagram
GEOMETRY FACT
ANGLE RELATIONSHIP
NAME
Vertical angles are congruent and
opposite each other, formed by 2
intersecting lines.
Vertical Angle
vert. s
a  b or ma  mb
Angles on a Line/ Parts of a straight angle
The sum of the adjacent angles on a line is
180⁰.
Adjacent angles: angles next to each
other sharing a 1 side
C
D
b°
a°
c°
A
B
Angles on a Line
s on a line
E
BAC  CAD  DAE  180
Straight angle: an angle of 180⁰ with 2
sides facing in opposite directions.
Supplementary angles: two angles that
form a linear pair that have a sum of 180.⁰
One angle is a supplement of the other
angle.
a  b  c  180
ao
SUPPLEMENTARY
ANGLES
bo
𝒂 + 𝒃 = 𝟏𝟖𝟎
(2 Angles on a Line)
Supplementary angles add to 180⁰.
Angles at a Point: sum of the measures of
all angles formed by three or more rays
with the same vertex is 360˚.
Angles at a Point
s at a point
ABC  DBC  CBA  360
B
Angle Sum of a Triangle: the sum of the 3
interior angles of any triangle is 180˚.
C
A
Angle Sum of a Triangle
 sum of 
A  B  C  180
Exterior angle of a triangle is equal to the
sum of the measures of two opposite
interior angles of a triangle.
Exterior Angle of a
Triangle
ext.  of 
Exterior angle is formed by extending one
of the sides of the triangle.
A  C  BDC
Angle sum of a Right Triangle: when one
angle of a triangle is a right angle, the sum
of the measures of the other two angles is
90˚.
Complementary angles: two angles with a
sum of 90˚.
Angle sum of a Right
Triangle
 sum of rt. 
COMPLEMENTARY
ANGLES
Diagram
GEOMETRY FACT
Perpendicular lines: when two lines lie in
the same plane and intersect to form right
angles.
ANGLE RELATIONSHIP
NAME
Perpendicular Lines
Q.
F
•
G
•
QR  FG
.R
Parallel lines: two lines that lie in the
same plane that never intersect and are
the same distance apart.
Line m1 is parallel
to m2
Parallel Lines
m1 / / m2
Equidistant: 2 objects the same distance
apart
Corresponding Angles: when a transversal
intersects two parallel lines then the
measures of the corresponding angles are
equal.
Corresponding angles
Same side of transversal
Same side of 2 // lines
Converse: If a transversal intersects two
lines such that the measures of the
corresponding angles are equal, then the
lines are parallel.
Alternate Interior Angles: when a
transversal intersects two parallel lines,
then the measures of alternate interior
angles are equal.
Alternate Interior
Angles
Opposite sides of
transversal
In-between the 2 // lines
Converse: If a transversal intersects two
lines such that measures of the alternate
interior angles are equal, then the lines
are parallel.
Alternate Exterior Angles: when a
transversal intersects two parallel lines,
then the measures of alternate exterior
angles are equal.
Alternate Exterior
Angles
Opposite sides of
transversal
Outside of the 2 // lines
Converse: If a transversal intersects two
lines such that measures of the alternate
exterior angles are equal, then the lines
are parallel.
If a transversal intersects two parallel
lines, any pair of angles is either
CONGRUENT
or SUPPLEMENTARY
equal in measure or
add to 180⁰
If a and b are created by parallel
lines cut by a transversal, then
a + b  180 or a  b
General understanding
of Parallel Lines angle
relationships