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Chapter 8 Vocabulary
http://www.mathopenref.com/cong
ruentlines.html
http://www.themathlab.com/dictionary/awords/awords.htm
http://www.themathlab.com/diction
ary/pwords/pwords.htm
Point, Line, Plane
• point An undefined geometric term: a point
represents a location and has no size.
• line An undefined geometric term. It is
represented by a straight line with two
arrowheads indicating line extends forever.
AB
BA
• plane An undefined geometric term. In
Euclidean Geometry, a plane is a flat surface
that extends infinitely in all directions.
Length
Line segment
• Length The distance between two points
• Line segment The points A and B
along with the points on segment
between A and B. Also called segments.
Ray
• ray A part of a line
which begins at some
point and goes on
forever in a particular
direction.
The ray with endpoint A
containing B is denoted
AB
.
Angle
• angle The union of two rays with the same endpoint.
The rays are the sides and the common endpoint is
called the vertex.
BAC
Vertex
• vertex (plural vertices). The point of
intersection of the sides of an angle.
Congruent
• Congruent Segments
Line segments that have the same length.
• Congruent Angles
Angles that have the same measure.
http://www.mathopenref.com/congruentlines.html
parallel lines
• Two lines in a plane are parallel if they
have no points in common or are identical.
NOTE: two common symbols used to
indicate parallel lines are the extra
arrowheads placed on the lines as you see
in the example above and also the ||
symbol.
perpendicular
• perpendicular The
name given to rays,
segments, or lines
that form right angles.
Right Angle: An angle
whose measure is 90°. A
right angle will always be
drawn with a small square
at its vertex.
Objective - To identify angles as vertical,
adjacent, complementary and
supplementary.
Plane - is a flat surface that
extends in all directions .
Vertical Angles
• Two angles formed by two intersecting
lines: opposite angles. Vertical angles will
always be congruent.
adjacent angles
• adjacent angles Two nonstraight and
nonzero angles with a common side
interior to the angle formed by the
noncommon sides.
Linear Pair
• linear pair Angles that have a common
side, and whose noncommon sides are
opposite rays. Linear pairs add to 180
degrees.
straight angle An angle whose
measure is 180°.
Supplementary Angles - Angles whose
sum is 180 .
k
t
mk  mt  180
b
c
mb  mc  180
Supplementary
angles may not
be adjacent.
Find the measure of the missing angle.
137
x
50
y
x  50  180
50 50
x  130
y  137  180
x  130
y  43
137  137
y  43
Find the supplement of the following...
1) 18
162
5) 148
32
2) 104
76
6) 62
118
3) 31
149
7) 159
21
4) 75
105
8) 179
1
Complementary Angles - Angles whose
sum is 90 .
a
b
ma  mb  90
x
y
mx  my  90
Complementary
angles may not
be adjacent.
Find the complement of the angle measures below.
1) 20
70
5) 15
75
2) 59
31
6) 57
33
3) 50
40
7) 43
47
4) 62
28
8) 100
Has no
complement
Parallel Lines - Lines in the same plane that
do not intersect.
B
A
AB CD
D
C
Intersecting Lines
C
B
A
D
Vertical Angles - Formed by intersecting lines.
Opposite angles (vertical angles)
are always congruent.
Adjacent Angles -Angels that share a common
vertex and side.
Find the measure of the missing angle.
x
40
x  40  90
40 40
x  50
x  50
Find the missing angles.
1)
A
2)
x
y
115
47
B
C
E
z
D
mx  65
my  115
mz  65
mABC  133
mCBD  47
mEBD  133
Vertical Angles
60
1
120
2
4
3
60
120
Characteristics of Vertical Angles
• Vertical Angles are Congruent Angles.
• Vertical Angles are Non-adjacent Angles.
• Adjacent Angles are Supplementary.
Supplementary Angles
H
G
E
F
M
______ and ________ are supplementary.
_____and _______are a linear pair.
80
N
100
triangle sum theorem
– The sum of the interior angles of any triangle is
equal to 180 degrees.
Euclid’s Postulates
• Euclid’s first postulate:
Through any two points, there is exactly
one line.
P
Q
For your information only ,
Undefined Term
• A word that does not have a formal
definition, but there is agreement about
what the word means.
• intersecting planes
Two planes that
contain the same line.
EX:
• alternate interior
angles Angles formed by two
lines cut by a transversal. They
are between the two lines and
on alternate sides of the
transversal.
•
• Angles three and five are
alternate interior angles as are
angles four and six.
• When the two lines cut by the
transversal are parallel, the
alternate interior angles will be
congruent.
parallelogram
• A quadrilateral with two pairs of parallel
sides.
• perpendicular bisector method A
method for finding the center of a circle
that involves drawing perpendicular
bisectors of two chords. You can use this
method to perform the really cool trick of
drawing a circle through any three noncolinear points.