Download acute angle adjacent angles angle angle bisector

Vocabulary Flash Cards
acute angle
Chapter 1 (p. 39)
angle
Chapter 1 (p. 42)
between
axiom
Chapter 1 (p. 12)
collinear points
Chapter 1 (p. 4)
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Chapter 1 (p. 48)
angle bisector
Chapter 1 (p .38)
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adjacent angles
Chapter 1 (p. 14)
complementary angles
Chapter 1 (p. 48)
Big Ideas Math Geometry
Vocabulary Flash Cards
Two angles that share a common vertex and side,
but have no common interior points

An angle that has a measure greater than 0 and

less than 90
common side
5
A
6
common vertex
5 and 6 are adjacent angles.
A ray that divides an angle into two angles that are
congruent
A set of points consisting of two different rays that
have the same endpoint
X
C
A, BAC , CAB,
or 1
W
Y
vertex
sides
1
A
Z

YW bisects XYZ , so XYW  ZYW .
When three points are collinear, one point is
between the other two.
B
A rule that is accepted without proof
The Segment Addition Postulate states that if B is
between A and C, then AB  BC  AC.
A
B
C
Point B is between points A and C.

Two angles whose measures have a sum of 90
B
C
A
58°
32°
Points that lie on the same line
A
B
C
A, B, and C are collinear.
D
BAC and CAB are complementary angles.
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Big Ideas Math Geometry
Vocabulary Flash Cards
congruent angles
Chapter 1 (p. 40)
construction
Chapter 1 (p. 13)
coplanar points
Chapter 1 (p. 4)
distance
Chapter 1 (p. 12)
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congruent segments
Chapter 1 (p. 13)
coordinate
Chapter 1 (p. 12)
defined terms
Chapter 1 (p. 5)
endpoints
Chapter 1 (p. 5)
Big Ideas Math Geometry
Vocabulary Flash Cards
Two angles that have the same measure
Line segments that have the same length
5 in.
A
5 in.
B
C
D
A
30°
30°
B
AB  CD
A  B
A real number that corresponds to a point on a line
A
B
x1
x2
coordinates of points
Terms that can be described using known words,
such as point or line
A geometric drawing that uses a limited set of
tools, usually a compass and a straightedge
A
B
C
D
Points that lie in the same plane
A
Line segment and ray are two defined terms.
M
C
B
A, B, and C are coplanar.
Points that represent the ends of a line segment or
ray
endpoint
endpoint
A
A
B
x1
A
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AB
B
x2
AB = x2 − x1
endpoint
All rights reserved.
The absolute value of the difference of two
coordinates on a line
B
Big Ideas Math Geometry
Vocabulary Flash Cards
exterior of an angle
interior of an angle
Chapter 1 (p. 38)
Chapter 1 (p. 38)
intersection
line
Chapter 1 (p. 4)
Chapter 1 (p. 6)
line segment
Chapter 1 (p. 5)
measure of an angle
Chapter 1 (p. 39)
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linear pair
Chapter 1 (p. 50)
midpoint
Chapter 1 (p. 20)
Big Ideas Math Geometry
Vocabulary Flash Cards
The region that contains all the points between the
sides of an angle
The region that contains all the points outside of an
angle
exterior
interior
A line has one dimension. It is represented by a
line with two arrowheads, but it extends without
end.
The set of points two or more geometric figures
have in common
m
A
A
B
n
line , line AB (AB),
or line BA (BA)
The intersection of two
different lines is a point.
Two adjacent angles whose noncommon sides are
opposite rays
Consists of two endpoints and all the points
between them
common side
endpoint
endpoint
A
B
1 2
noncommon side noncommon side
1 and 2 are a linear pair.
The point that divides a segment into two
congruent segments
M
B
AB.
So, AM  MB and AM  MB.
0 10
180 170 1 20
60
M is the midpoint of
A
O
B
170 180
60
0 1 20 10 0
15
0 30
14 0
4
80 90 10 0
70 10 0 90 80 110 1
70
2
60 0 110
60 0 13
2
50 0 1
50 0
3
1
3
15 0 4
01 0
40
A
The absolute value of the difference between the
real numbers matched with the two rays that form
the angle on a protractor
mAOB  140
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Big Ideas Math Geometry
Vocabulary Flash Cards
obtuse angle
opposite rays
Chapter 1 (p. 5)
Chapter 1 (p. 39)
plane
point
Chapter 1 (p. 4)
Chapter 1 (p. 4)
postulate
ray
Chapter 1 (p. 5)
Chapter 1 (p. 12)
right angle
Chapter 1 (p. 39)
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segment
Chapter 1 (p. 5)
Big Ideas Math Geometry
Vocabulary Flash Cards


If point C lies on AB between A and B, then CA

and CB are opposite rays.
A C

An angle that has a measure greater than 90 and

less than 180
B


CA and CB are opposite rays.
A location in space that is represented by a dot and
has no dimension
A
A
A flat surface made up of points that has two
dimensions and extends without end, and is
represented by a shape that looks like a floor or a
wall
point A
A
B
M
C
plane M, or plane ABC

AB is a ray
if it consists of the endpoint A and all
points on AB that lie on the same side of A as B.
A rule that is accepted without proof
The Segment Addition Postulate states that if B is
between A and C, then AB  BC  AC.
endpoint
A
B

AB
Consists of two endpoints and all the points
between them
endpoint
endpoint
A
B

An angle that has a measure of 90
A
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Big Ideas Math Geometry
Vocabulary Flash Cards
segment bisector
Chapter 1 (p. 20)
straight angle
Chapter 1 (p. 39)
undefined terms
Chapter 1 (p. 4)
sides of an angle
Chapter 1 (p. 38)
supplementary angles
Chapter 1 (p. 48)
vertex of an angle
Chapter 1 (p. 38)
vertical angles
Chapter 1 (p. 50)
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Big Ideas Math Geometry
Vocabulary Flash Cards
The rays of an angle
A point, ray, line, line segment, or plane that
intersects the segment at its midpoint
C
C
sides
M
A
B
D
A
B

CD is a segment bisector of AB.
So, AM  MB and AM  MB.

Two angles whose measures have a sum of 180
An angle that has a measure of 180
M

A
75° 105°
J
K
L
JKM and LKM are supplementary angles.
The common endpoint of the two rays that form an
angle
C
Words that do not have formal definitions, but
there is agreement about what they mean
In geometry, the words point, line, and plane are
undefined terms.
vertex
A
B
Two angles whose sides form two pairs of opposite
rays
3
4
5
6
3 and 6 are vertical angles.
4 and 5 are vertical angles.
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Big Ideas Math Geometry
Vocabulary Flash Cards
biconditional statement
Chapter 2 (p. 69)
conditional statement
Chapter 2 (p. 66)
contrapositive
Chapter 2 (p. 67)
counterexample
Chapter 2 (p. 77)
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conclusion
Chapter 2 (p. 66)
conjecture
Chapter 2 (p. 76)
converse
Chapter 2 (p. 67)
deductive reasoning
Chapter 2 (p. 78)
Big Ideas Math Geometry
Vocabulary Flash Cards
The “then” part of a conditional statement written
in if-then form
A statement that contains the phrase “if and only
if”
If you are in Houston, then you are in Texas.
Two lines intersect to form a right angle if and
only if they are perpendicular lines.
hypothesis, p
conclusion, q
An unproven statement that is based on
observations
A logical statement that has a hypothesis and a
conclusion
Conjecture: The sum of any three consecutive
integers is three times the second
number.
If you are in Houston, then you are in Texas.
The statement formed by exchanging the
hypothesis and conclusion of a conditional
statement
The statement formed by negating both the
hypothesis and conclusion of the converse of a
conditional statement
Statement: If you are a guitar player, then you are a
musician.
Converse: If you are a musician, then you are a
guitar player.
Statement: If you are a guitar player, then you are a
musician.
Contrapositive: If you are not a musician, then you
are not a guitar player.
A process that uses facts, definitions, accepted
properties, and the laws of logic to form a logical
argument
A specific case for which a conjecture is false
You use deductive reasoning to write geometric
proofs.
hypothesis, p
conclusion, q
Conjecture: The sum of two numbers is always
more than the greater number.
Counterexample: 2  (3)  5
5   2
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Big Ideas Math Geometry
Vocabulary Flash Cards
equivalent statements
Chapter 2 (p. 67)
hypothesis
flowchart proof (flow proof)
Chapter 2 (p. 106)
if-then form
Chapter 2 (p. 66)
Chapter 2 (p. 66)
inductive reasoning
Chapter 2 (p. 76)
line perpendicular to a plane
Chapter 2 (p. 86)
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inverse
Chapter 2 (p. 67)
negation
Chapter 2 (p. 66)
Big Ideas Math Geometry
Vocabulary Flash Cards
A type of proof that uses boxes and arrows to show
the flow of a logical argument
Two related conditional statements that are both
true or both false
A conditional statement and its contrapositive are
equivalent statements
A conditional statement in the form “if p, then q”,
where the “if” part contains the hypothesis and the
“then” part contains the conclusion
The “if” part of a conditional statement written in
if-then form
If you are in Houston, then you are in Texas.
If you are in Houston, then you are in Texas.
hypothesis, p
hypothesis, p
conclusion, q
conclusion, q
The statement formed by negating both the
hypothesis and conclusion of a conditional
statement
Statement: If you are a guitar player, then you are a
musician.
Inverse: If you are not a guitar player, then you are
not a musician.
The opposite of a statement
A process that includes looking for patterns and
making conjectures
Given the number pattern 1, 5, 9, 13, …, you can
use inductive reasoning to determine that the next
number in the pattern is 17.
A line that intersects the plane in a point and is
perpendicular to every line in the plane that
intersects it at that point
t
If a statement is p, then the negation is “not p,”
written ~p.
p
Statement: The ball is red.
Negation: The ball is not red.
A
q
Line t is perpendicular to plane P.
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Big Ideas Math Geometry
Vocabulary Flash Cards
paragraph proof
Chapter 2 (p. 108)
proof
perpendicular lines
Chapter 2 (p. 68)
theorem
Chapter 2 (p. 100)
truth table
Chapter 2 (p. 70)
Chapter 2 (p. 101)
truth value
Chapter 2 (p. 70)
two column proof
Chapter 2 (p. 100)
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Big Ideas Math Geometry
Vocabulary Flash Cards
Two lines that intersect to form a right angle
A style of proof that presents the statements and
reasons as sentences in a paragraph, using words to
explain the logical flow of an argument
m
⊥m
A statement that can be proven
A logical argument that uses deductive reasoning
to show that a statement is true
Vertical angles are congruent.
A value that represents whether a statement is
true (T) or false (F)
See truth table.
A table that shows the truth values for a
hypothesis, conclusion, and a conditional statement
Conditional
p
q
pq
T
T
T
T
F
F
F
T
T
F
F
T
A type of proof that has numbered statements and
corresponding reasons that show an argument in a
logical order
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Big Ideas Math Geometry
Vocabulary Flash Cards
alternate exterior angles
Chapter 3 (p. 128)
consecutive interior angles
Chapter 3 (p. 128)
directed line segment
Chapter 3 (p. 156)
parallel lines
Chapter 3 (p. 126)
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alternate interior angles
Chapter 3 (p. 128)
corresponding angles
Chapter 3 (p. 128)
distance from a point to a
line
Chapter 3 (p. 148)
parallel planes
Chapter 3 (p. 126)
Big Ideas Math Geometry
Vocabulary Flash Cards
Two angles that are formed by two lines and a
transversal that are between the two lines and on
opposite sides of the transversal
Two angles that are formed by two lines and a
transversal that are outside the two lines and on
opposite sides of the transversal
t
t
1
4
5
8
4 and 5 are alternate interior angles.
Two angles that are formed by two lines and a
transversal that are in corresponding positions
1 and 8 are alternate exterior angles.
Two angles that are formed by two lines and a
transversal that lie between the two lines and on
the same side of the transversal
t
2
t
6
3
5
2 and 6 are corresponding angles.
The length of the perpendicular segment from the
point to the line
A
3 and 5 are consecutive interior angles.
A segment that represents moving from point A to
point B is called the directed line segment AB.
8
k
y
B(6, 8)
6
4
B
2
The distance between point A and the line k is AB.
A(3, 2)
2
Planes that do not intersect
4
6
8x
Coplanar lines that do not intersect
S
m
 m
T
ST
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Big Ideas Math Geometry
Vocabulary Flash Cards
perpendicular bisector
Chapter 3 (p. 149)
skew lines
Chapter 3 (p. 126)
transversal
Chapter 3 (p. 128)
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Big Ideas Math Geometry
Vocabulary Flash Cards
Lines that do not intersect and are not coplanar
A line that is perpendicular to a segment at its
midpoint
p
n
n
A
Lines n and p are skew lines.
P
M
Q
Line n is the perpendicular bisector of PQ.
A line that intersects two or more coplanar lines at
different points.
t
transversal t
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Big Ideas Math Geometry
Vocabulary Flash Cards
angle of rotation
Chapter 4 (p. 190)
center of rotation
Chapter 4 (p. 190)
component form
Chapter 4 (p. 174)
congruence transformation
Chapter 4 (p. 201)
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center of dilation
Chapter 4 (p. 208)
center of symmetry
Chapter 4 (p. 193)
composition of
transformations
Chapter 4 (p. 176)
congruent figures
Chapter 4 (p. 200)
Big Ideas Math Geometry
Vocabulary Flash Cards
The fixed point in a dilation
The angle that is formed by rays drawn from the
center of rotation to a point and its image
P′
P
C
R′
R
Q
Q′
R
40°
center of dilation
Q
Q′
R′
angle of
rotation
center of rotation
The center of rotation in a figure that has rotational
symmetry
P
The fixed point in a rotation
R′
The parallelogram has
rotational symmetry. The
center is the intersection

of the diagonals. A 180
rotation about the center
maps the parallelogram
onto itself.
R
40°
Q
Q′
center of rotation
The combination of two or more transformations to
form a single transformation
A glide reflection is an example of a composition
of transformations.
angle of
rotation
P
A form of a vector that combines the horizontal
and vertical components
Q
2 units up vertical
P
component
4 units right
horizontal component
The component form of
Geometric figures that have the same size and
shape
B
A
E
C
F

PQ is 4, 2 .
A transformation that preserves length and angle
measure
Translations, reflections, and rotations are three
types of congruence transformations.
D
ABC  DEF
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Big Ideas Math Geometry
Vocabulary Flash Cards
dilation
Chapter 4 (p. 208)
glide reflection
Chapter 4 (p. 184)
image
line of reflection
Chapter 4 (p. 182)
All rights reserved.
Chapter 4 (p. 208)
horizontal component
Chapter 4 (p. 174)
initial point
Chapter 4 (p. 174)
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enlargement
Chapter 4 (p. 174)
line symmetry
Chapter 4 (p. 185)
Big Ideas Math Geometry
Vocabulary Flash Cards
A dilation in which the scale factor is greater than
1
A transformation in which a figure is enlarged or
reduced with respect to a fixed point
A dilation with a scale factor of 2 is an
enlargement.
P′
P
C
Q
Q′
R
center of dilation
R′
Scale factor of dilation is
The horizontal change from the starting point of a
vector to the ending point
CP
.
CP
A transformation involving a translation followed
by a reflection
Q
Q′
P′
P
Q″
4 units right
P″
horizontal component
Q
P
k
The starting point of a vector
A figure that results from the transformation of a
geometric figure
K
B
6
y
C′
B′
4
A
J

Point J is the initial point of JK .
A figure in the plane has line symmetry when the
figure can be mapped onto itself by a reflection in
a line.
C
D
D′
A′
2
6
4
x
ABC D is the image of ABCD after a translation.
A line that acts as a mirror for a reflection
4
y
A
B
2
m
C
C′
B′
6
x
A′

Two lines of symmetry
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ABC  is the image of
in the line m.
ABC after a reflection
Big Ideas Math Geometry
Vocabulary Flash Cards
line of symmetry
Chapter 4 (p. 185)
reduction
Chapter 4 (p. 208)
rigid motion
Chapter 4 (p. 176)
rotational symmetry
Chapter 4 (p. 193)
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preimage
Chapter 4 (p. 174)
reflection
Chapter 4 (p. 182)
rotation
Chapter 4 (p. 190)
scale factor
Chapter 4 (p. 208)
Big Ideas Math Geometry
Vocabulary Flash Cards
The original figure before a transformation
B
6
y
A line of reflection that maps a figure onto itself
C
C′
B′
4
A
D
D′
A′
2
4
x
6
ABCD is the preimage and ABC D is the image
after a translation.
A transformation that uses a line like a mirror to
reflect a figure
4
A dilation in which the scale factor is greater than
0 and less than 1
y
A
A dilation with a scale factor of
B
2
m
C
x
6
A′
ABC  is the image of
in the line m.
1
is a reduction.
2
B′
C′

Two lines of symmetry
ABC after a reflection
A transformation in which a figure is turned about
a fixed point
A transformation that preserves length and angle
measure
R
R′
Translations, reflections, and rotations are three
types of rigid motions.
40°
Q
Q′
angle of
rotation
center of
rotation
P
The ratio of the lengths of the corresponding sides
of the image and the preimage of a dilation
P′
P
C
Q
Q′
R
center of dilation
R′
Scale factor of dilation is
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CP
.
CP
A figure has rotational symmetry when the figure

can be mapped onto itself by a rotation of 180 or
less about the center of the figure.
The parallelogram has rotational
symmetry. The center is the
intersection of the diagonals.

A 180 rotation about the
center maps the parallelogram
onto itself.
Big Ideas Math Geometry
Vocabulary Flash Cards
similar figures
similarity transformation
Chapter 4 (p. 216)
terminal point
Chapter 4 (p. 216)
transformation
Chapter 4 (p. 174)
translation
Chapter 4 (p. 174)
Chapter 4 (p. 174)
vector
Chapter 4 (p. 174)
vertical component
Chapter 4 (p. 174)
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Big Ideas Math Geometry
Vocabulary Flash Cards
A dilation or a composition of rigid motions and
dilations
6
A(−4, 1)
B(−2, 2)
y
B″(6, 6)
A″(2, 4)
4
2
Geometric figures that have the same shape, but
not necessarily the same size
y
Q
P
2
B′(3, 3) C″(6, 4)
A′(1, 2) C′(3, 2)
−4
−2
W
−2
4
C(−2, 1)
−4
X
Y
2
4
6
ABC is the image of ABC after a
6
x
Z
8 x
S
R
Trapezoid PQRS is similar to trapezoid WXYZ.
similarity transformation.
A function that moves or changes a figure in some
way to produce a new figure
The ending point of a vector
K
Four basic transformations are translations,
reflections, rotations, and dilations.
J

Point K is the terminal point of JK .
A quantity that has both direction and magnitude,
and is represented in the coordinate plane by an
arrow drawn from one point to another
A transformation that moves every point of a
figure the same distance in the same direction
y
K
A′
A
3
B′
C
C′
J

JK with initial point J and terminal point K.
2
4
B
6
8 x
ABC is the image of ABC after a translation.
The vertical change from the starting point of a
vector to the ending point
P
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Q
2 units up vertical
component
Big Ideas Math Geometry
Vocabulary Flash Cards
base angles of an isosceles
triangle
base of an isosceles triangle
Chapter 5 (p. 252)
Chapter 5 (p. 252)
coordinate proof
Chapter 5 (p. 284)
corresponding parts
Chapter 5 (p. 240)
hypotenuse
Chapter 5 (p. 264)
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corollary to a theorem
Chapter 5 (p. 235)
exterior angles
Chapter 5 (p. 233)
interior angles
Chapter 5 (p. 233)
Big Ideas Math Geometry
Vocabulary Flash Cards
The side of an isosceles triangle that is not one of
the legs
leg
The two angles adjacent to the base of an isosceles
triangle
leg
leg
leg
base
angles
base
base
A statement that can be proved easily using the
theorem
A style of proof that involves placing geometric
figures in a coordinate plane
The Corollary to the Triangle Sum Theorem states
that the acute angles of a right triangle are
complementary.
Angles that form linear pairs with the interior
angles of a polygon
A pair of sides or angles that have the same
relative position in two congruent figures
B
Corresponding angles
B
A  D, B  E, C  F
C
A
E
A
C
Corresponding sides
AB  DE , BC  EF , AC  DF
F
D
exterior angles
Angles of a polygon
The side opposite the right angle of a right triangle
hypotenuse
B
A
C
interior angles
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Big Ideas Math Geometry
Vocabulary Flash Cards
legs of an isosceles triangle
Chapter 5 (p. 252)
legs of a right triangle
Chapter 5 (p. 264)
vertex angle
Chapter 5 (p. 252)
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Big Ideas Math Geometry
Vocabulary Flash Cards
The sides adjacent to the right angle of a right
triangle
The two congruent sides of an isosceles triangle
leg
leg
leg
leg
The angle formed by the legs of an isosceles
triangle
vertex angle
leg
leg
base
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Big Ideas Math Geometry
Vocabulary Flash Cards
altitude of a triangle
Chapter 6 (p. 321)
circumcenter
Chapter 6 (p. 310)
equidistant
Chapter 6 (p. 302)
indirect proof
Chapter 6 (p. 336)
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centroid
Chapter 6 (p. 320)
concurrent
Chapter 6 (p. 310)
incenter
Chapter 6 (p. 313)
median of a triangle
Chapter 6 (p. 320)
Big Ideas Math Geometry
Vocabulary Flash Cards
The point of concurrency of the three medians of a
triangle
The perpendicular segment from a vertex of a
triangle to the opposite side or to the line that
contains the opposite side
B
Q
D
P
A
F
altitude from
Q to PR
E
C
P is the centroid of
Q
ABC.
Three or more lines, rays, or segments that
intersect in the same point
P
R
P
R
The point of concurrency of the three
perpendicular bisectors of a triangle
B
j
k
P
P
A
Lines j, k, and  are concurrent.
The point of concurrency of the angle bisectors of
a triangle
C
P is the circumcenter of
ABC.
A point is equidistant from two figures when it is
the same distance from each figure.
B
X
Z
Y
P
X is equidistant from Y and Z.
A
C
P is the incenter of
ABC.
A segment from a vertex of a triangle to the
midpoint of the opposite side
A style of proof in which you temporarily assume
that the desired conclusion is false, then reason
logically to a contradiction
B
This proves that the original statement is true.
A
D
BD is a median of
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C
ABC.
Big Ideas Math Geometry
Vocabulary Flash Cards
midsegment of a triangle
Chapter 6 (p. 330)
orthocenter
Chapter 6 (p. 321)
point of concurrency
Chapter 6 (p. 310)
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Big Ideas Math Geometry
Vocabulary Flash Cards
The point of concurrency of the lines containing
the altitudes of a triangle
A segment that connects the midpoints of two
sides of a triangle
B
D
A
M
E
P
G
A
C
F
G is the orthocenter of
B
ABC.
N
The midsegments of
and
C
ABC are MP, MN,
NP.
The point of intersection of concurrent lines, rays,
or segments
j
k
P
P is the point of concurrency for lines j, k,
and .
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Big Ideas Math Geometry
Vocabulary Flash Cards
base angles of a trapezoid
Chapter 7 (p. 398)
diagonal
Chapter 7 (p. 360)
equilateral polygon
Chapter 7 (p. 361)
kite
All rights reserved.
Chapter 7 (p. 398)
equiangular polygon
Chapter 7 (p. 361)
isosceles trapezoid
Chapter 7 (p. 398)
legs of a trapezoid
Chapter 7 (p. 401)
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bases of a trapezoid
Chapter 7 (p. 398)
Big Ideas Math Geometry
Vocabulary Flash Cards
The parallel sides of a trapezoid
B
base
Either pair of consecutive angles whose common
side is a base of a trapezoid
C
B
A
base angles
base
C
D
base
A
A polygon in which all angles are congruent
D
base
base angles
A segment that joins two nonconsecutive vertices
of a polygon
C
B
D
diagonals
A
E
A trapezoid with congruent legs
A polygon in which all sides are congruent
The nonparallel sides of a trapezoid
A quadrilateral that has two pairs of consecutive
congruent sides, but opposite sides are not
congruent
B
leg
A
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C
leg
D
Big Ideas Math Geometry
Vocabulary Flash Cards
midsegment of a trapezoid
Chapter 7 (p. 400)
rectangle
Chapter 7 (p. 388)
rhombus
Chapter 7 (p. 388)
parallelogram
Chapter 7 (p. 368)
regular polygon
Chapter 7 (p. 361)
square
Chapter 7 (p. 388)
trapezoid
Chapter 7 (p. 398)
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Big Ideas Math Geometry
Vocabulary Flash Cards
A quadrilateral with both pairs of opposite sides
parallel
Q
The segment that connects the midpoints of the
legs of a trapezoid
R
midsegment
P
S
PQRS
A convex polygon that is both equilateral and
equiangular
A parallelogram with four right angles
A parallelogram with four congruent sides and four
right angles
A parallelogram with four congruent sides
A quadrilateral with exactly one pair of parallel
sides
B
base
leg
leg
A
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C
base
D
Big Ideas Math Geometry
Vocabulary Flash Cards
angle of depression
Chapter 9 (p. 497)
cosine
inverse cosine
Chapter 9 (p. 502)
inverse tangent
Chapter 9 (p. 502)
All rights reserved.
Chapter 9 (p. 490)
geometric mean
Chapter 9 (p. 494)
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angle of elevation
Chapter 9 (p. 480)
inverse sine
Chapter 9 (p. 502)
Law of Cosines
Chapter 9 (p. 511)
Big Ideas Math Geometry
Vocabulary Flash Cards
The angle that an upward line of sight makes with
a horizontal line
The angle that a downward line of sight makes with
a horizontal line
angle of depression
angle of elevation
The positive number x that satisfies
2
So, x  ab and x 
a x

x b
A trigonometric ratio for acute angles that involves
the lengths of a leg and the hypotenuse of a right
triangle
B
leg
opposite
∠A
ab .
The geometric mean of 4 and 16 is
4  16, or 8.
C
cos A 
An inverse trigonometric ratio, abbreviated as
sin
1
leg adjacent
to ∠A
A
length of leg adjacent to A AC

length of hypotenuse
AB
An inverse trigonometric ratio, abbreviated as
cos 1
For acute angle A, if sin A  y, then
1
B
C
A
For acute angle A, if cos A  z, then
cos 1 z  mA.
sin y  mA.
For
hypotenuse
BC
sin1
 mA
AB
ABC with side lengths of a, b, and c,
a 2  b2  c 2  2bc cos A,
b2  a 2  c 2  2ac cos B, and
c 2  a 2  b2  2ab cos C.
B
cos1
A
C
AC
 mA
AB
An inverse trigonometric ratio, abbreviated as
tan 1
For acute angle A, if tan A  x, then
tan 1 x  mA.
B
tan1
A
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C
BC
 mA
AC
Big Ideas Math Geometry
Vocabulary Flash Cards
Law of Sines
Chapter 9 (p. 509)
sine
Pythagorean triple
Chapter 9 (p. 464)
solve a right triangle
Chapter 9 (p. 494)
standard position
Chapter 9 (p. 462)
Chapter 9 (p. 503)
tangent
Chapter 9 (p. 488)
trigonometric ratio
Chapter 9 (p. 488)
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Big Ideas Math Geometry
Vocabulary Flash Cards
A set of three positive integers a, b, and c that
2
2
2
satisfy the equation c  a  b
For
ABC with side lengths of a, b, and c,
sin A sin B sin C


and
a
b
c
a
b
c


.
sin A sin B sin C
Common Pythagorean triples:
3, 4, 5
5, 12, 13
8, 15, 17
7, 24, 25
To find all unknown side lengths and angle
measures of a right triangle
A trigonometric ratio for acute angles that involves
the lengths of a leg and the hypotenuse of a right
triangle
B
leg
opposite
∠A
You can solve a right triangle when you know
either of the following.
 two side lengths
 one side length and the measure of one
acute angle
C
sin A 
A trigonometric ratio for acute angles that involves
the lengths of the legs of a right triangle
B
leg
opposite
∠A
C
tan A 
hypotenuse
A
leg adjacent
to ∠A
length of leg opposite A BC

length of hypotenuse
AB
A right triangle is in standard position when the
hypotenuse is a radius of the circle of radius 1 with
center at the origin, one leg lies on the x-axis, and
the other leg is perpendicular to the x-axis.
y
hypotenuse
B
0.5
leg adjacent
to ∠A
A
−0.5 A
length of leg opposite A
BC

length of leg adjacent to A AC
0.5 C
x
−0.5
A ratio of the lengths of two sides in a right
triangle
Three common trigonometric ratios are sine,
cosine, and tangent.
3
C
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3
BC

AC 4
BC 3
sin A 

AB 5
AC 4
cos A 

AB 5
tan A 
B
5
4
A
Big Ideas Math Geometry
Vocabulary Flash Cards
adjacent arcs
Chapter 10 (p. 539)
central angle of a circle
Chapter 10 (p. 538)
circle
Chapter 10 (p. 530)
circumscribed circle
Chapter 10 (p. 556)
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center of a circle
Chapter 10 (p. 530)
chord of a circle
Chapter 10 (p. 530)
circumscribed angle
Chapter 10 (p. 564)
common tangent
Chapter 10 (p. 531)
Big Ideas Math Geometry
Vocabulary Flash Cards
The point from which all points on a circle are
equidistant
Arcs of a circle that have exactly one point in
common
A
B
P
C
circle with center P, or
P
A segment whose endpoints are on a circle
T
S
Q
P
chords
R

 are adjacent arcs.
AB and BC
An angle whose vertex is the center of a circle
P
C
Q
PCQ is a central angle of C.
An angle whose sides are tangent to a circle
The set of all points in a plane that are equidistant
from a given point
A
B
circumscribed C
angle
P
circle with center P, or
A line or segment that is tangent to two coplanar
circles
P
A circle that contains all the vertices of an
inscribed polygon
circumscribed
circle
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Big Ideas Math Geometry
Vocabulary Flash Cards
concentric circles
Chapter 10 (p. 531)
congruent circles
Chapter 10 (p. 540)
external segment
Chapter 10 (p. 571)
inscribed polygon
Chapter 10 (p. 556)
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congruent arcs
Chapter 10 (p. 540)
diameter
Chapter 10 (p. 530)
inscribed angle
Chapter 10 (p. 554)
intercepted arc
Chapter 10 (p. 554)
Big Ideas Math Geometry
Vocabulary Flash Cards
Arcs that have the same measure and arc of the
same circle or of congruent circles
Coplanar circles that have a common center
D E
C
80° 80°
B
F
  EF

CD
A chord that contains the center of a circle
Circles that can be mapped onto each other by a
rigid motion or a composition of rigid motions
diameter
4m
4m
P
Q
P  Q
An angle whose vertex is on a circle and whose
sides contain chords of the circle
A
inscribed
angle B
The part of a secant segment that is outside the
circle
R
external segment Q
secant segment
P
C
S
PR is a secant segment.
PQ is the external segment of PR.
An arc that lies between two lines, rays, or
segments
A polygon in which all of the vertices lie on a
circle
A
intercepted
arc
B
inscribed
polygon
C
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Big Ideas Math Geometry
Vocabulary Flash Cards
major arc
Chapter 10 (p. 538)
measure of a minor arc
Chapter 10 (p. 538)
point of tangency
Chapter 10 (p. 530)
secant
Chapter 10 (p. 530)
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measure of a major arc
Chapter 10 (p. 538)
minor arc
Chapter 10 (p. 538)
radius of a circle
Chapter 10 (p. 530)
secant segment
Chapter 10 (p. 571)
Big Ideas Math Geometry
Vocabulary Flash Cards
The measure of a major arc’s central angle
An arc with a measure greater than 180
A
50°
A
B
C

B
C
D
D
major arc ADB
  360  50  310
mADB
An arc with a measure less than 180

The measure of a minor arc’s central angle
A
A
minor arc AB
50°
B
C
C
mAB = 50°
B
D
D
A segment whose endpoints are the center and any
point on a circle
The point at which a tangent line intersects a circle
Q
radius
P
tangent B
A segment that contains a chord of a circle, and
has exactly one endpoint outside the circle
R
Q
P
point of
tangency
A
A line that intersects a circle in two points
secant
secant segment
S
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Big Ideas Math Geometry
Vocabulary Flash Cards
segments of a chord
Chapter 10 (p. 570)
similar arcs
Chapter 10 (p. 541)
subtend
Chapter 10 (p. 554)
tangent circles
Chapter 10 (p. 531)
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semicircle
Chapter 10 (p. 538)
standard equation of a circle
Chapter 10 (p. 576)
tangent of a circle
Chapter 10 (p. 530)
tangent segment
Chapter 10 (p. 571)
Big Ideas Math Geometry
Vocabulary Flash Cards
An arc with endpoints that are the endpoints of a
diameter
The segments formed from two chords that
intersect in the interior of a circle
S
Q
C
A
R
P
E
B
D
EA and EB are segments of chord AB, DE
 is a semicircle.
QSR
( x  h)2  ( y  k )2  r 2 , where r is the radius
and (h, k ) is the center
and EC are segments of chord DC.
Arcs that have the same measure
T
R
The standard equation of a circle with center (2, 3)
2
2
and radius 4 is ( x  2)  ( y  3)  16.
Q
U
S
 ~ TU

RS
A line in the plane of a circle that intersects the
circle at exactly one point
If the endpoints of a chord or arc lie on the sides of
an inscribed angle, the chord or arc is said to
subtend the angle.
A
inscribed
angle B
point of
tangency
intercepted
arc
C
tangent B
A
 subtends B.
AC
AC subtends B.
A segment that is tangent to a circle at an endpoint
Coplanar circles that intersect in one point
R
Q
P
tangent segment
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S
Big Ideas Math Geometry
Vocabulary Flash Cards
apothem of a regular polygon
Chapter 11 (p. 611)
axis of revolution
Chapter 11 (p. 620)
center of a regular polygon
Chapter 11 (p. 611)
chord of a sphere
Chapter 11 (p. 648)
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arc length
Chapter 11 (p. 595)
Cavalieri’s Principle
Chapter 11 (p. 626)
central angle of a regular
polygon
Chapter 11 (p. 611)
circumference
Chapter 11 (p. 594)
Big Ideas Math Geometry
Vocabulary Flash Cards
A portion of the circumference of a circle
Arc length of 
AB m 
AB

, or
2 r
360
m
AB
 2 r
Arc length of 
AB 
360
The distance from the center to any side of a
regular polygon
A
P
r
B
If two solids have the same height and the same
cross-sectional area at every level, then they have
the same volume.
apothem
The line around which a two-dimensional shape is
rotated to form a three-dimensional figure
The prisms below have equal heights h and equal
cross-sectional areas B at every level. By Cavalieri’s
Principle, the prisms have the same volume.
B
h
B
An angle formed by two radii drawn to
consecutive vertices of a polygon
The center of a polygon’s circumscribed circle
center
M
P
P
N
MPN is a central angle.
The distance around a circle
A segment whose endpoints are on a sphere
chord
r
d
C
C = π d = 2π r
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Big Ideas Math Geometry
Vocabulary Flash Cards
cross section
density
Chapter 11 (p. 619)
edge
face
Chapter 11 (p. 618)
great circle
Chapter 11 (p. 648)
net
All rights reserved.
Chapter 11 (p. 618)
lateral surface of a cone
Chapter 11 (p. 642)
polyhedron
Chapter 11 (p. 592)
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Chapter 11 (p. 628)
Chapter 11 (p. 618)
Big Ideas Math Geometry
Vocabulary Flash Cards
The amount of matter that an object has in a given
unit of volume
density 
mass
volume
A flat surface of a polyhedron
The intersection of a plane and a solid
plane
cross section
A line segment formed by the intersection of two
faces of a polyhedron
face
edge
Consists of all segments that connect the vertex
with points on the base edge of a cone
The intersection of a plane and a sphere such that
the plane contains the center of the sphere
lateral surface
great
circle
base
A solid that is bounded by polygons
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A two-dimensional pattern that can be folded to
form a three-dimensional figure
Big Ideas Math Geometry
Vocabulary Flash Cards
population density
Chapter 11 (p. 603)
radius of a regular polygon
Chapter 11 (p. 611)
similar solids
Chapter 11 (p. 630)
vertex of a polyhedron
Chapter 11 (p. 618)
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radian
Chapter 11 (p. 597)
sector of a circle
Chapter 11 (p. 604)
solid of revolution
Chapter 11 (p. 620)
volume
Chapter 11 (p. 626)
Big Ideas Math Geometry
Vocabulary Flash Cards
A unit of measurement for angles
45 

4
radians
A measure of how many people live within a given
area
population density 
The region bounded by two radii of the circle and
their intercepted arc
The radius of a polygon’s circumscribed circle
A
P
r
number of people
area of land
P
radius
N
B
sector APB
A three-dimensional figure that is formed by
rotating a two-dimensional shape around an axis
Two solids of the same type with equal ratios of
corresponding linear measures
The number of cubic units contained in the interior
of a solid
A point of a polyhedron where three or more edges
meet
3 ft
4 ft
vertex
6 ft
Volume  3(4)(6)  72ft 3
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Big Ideas Math Geometry
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC
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Big Ideas Math Geometry