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Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
acute angle
adjacent angles
angle
angle bisector
axiom
between
collinear points
complementary angles
Chapter 1 (p. 39) Chapter 1 (p. 48)
Chapter 1 (p .38) Chapter 1 (p. 42)
Chapter 1 (p. 12) Chapter 1 (p. 14)
Chapter 1 (p. 4) Chapter 1 (p. 48)
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
Two angles that share a common vertex and side, but have no common interior points
5 and 6 are adjacent angles.
An angle that has a measure greater than 0 and
less than 90
A ray that divides an angle into two angles that are congruent
YW
bisects ,XYZ so .XYW ZYW
A set of points consisting of two different rays that have the same endpoint
, , ,A BAC CAB
or 1
When three points are collinear, one point is between the other two.
Point B is between points A and C.
A rule that is accepted without proof
The Segment Addition Postulate states that if B is between A and C, then .AB BC AC
Two angles whose measures have a sum of 90
and BAC CAB are complementary angles.
Points that lie on the same line
A, B, and C are collinear.
common vertex
common side
65
A
Z
Y
X
W
A
BC
A
B
D
C
32°58°
A B C
B
C
A
sidesvertex
1
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
congruent angles
congruent segments
construction
coordinate
coplanar points
defined terms
distance
endpoints
Chapter 1 (p. 40) Chapter 1 (p. 13)
Chapter 1 (p. 13) Chapter 1 (p. 12)
Chapter 1 (p. 4) Chapter 1 (p. 5)
Chapter 1 (p. 12) Chapter 1 (p. 5)
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
Line segments that have the same length
AB CD
Two angles that have the same measure
A B
A real number that corresponds to a point on a line
A geometric drawing that uses a limited set of tools, usually a compass and a straightedge
Terms that can be described using known words, such as point or line
Line segment and ray are two defined terms.
Points that lie in the same plane
A, B, and C are coplanar.
Points that represent the ends of a line segment or ray
The absolute value of the difference of two coordinates on a line
C DA B
5 in. 5 in.
A30°
B30°
A B
x1 x2
coordinates of pointsA B
DC
AC
M
B
A B
endpoint endpoint
A B
endpoint
A AB
AB = �x2 − x1�
B
x1 x2
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
exterior of an angle
interior of an angle
intersection
line
line segment
linear pair
measure of an angle
midpoint
Chapter 1 (p. 38) Chapter 1 (p. 38)
Chapter 1 (p. 6) Chapter 1 (p. 4)
Chapter 1 (p. 5) Chapter 1 (p. 50)
Chapter 1 (p. 39) Chapter 1 (p. 20)
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
The region that contains all the points between the sides of an angle
The region that contains all the points outside of an angle
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
The intersection of two different lines is a point.
Two adjacent angles whose noncommon sides are opposite rays
1 and 2 are a linear pair.
Consists of two endpoints and all the points between them
The point that divides a segment into two congruent segments
M is the midpoint of AB.
So, AM MB AM MB and .
The absolute value of the difference between the real numbers matched with the two rays that form the angle on a protractor
140m AOB
interiorexterior
AB
line , line AB (AB),or line BA (BA)
mA
n
noncommon side noncommon side1 2
common side
A B
endpoint endpoint
A M B
9090
8010070
1106012050
130
40140
30150
2016
0
10 170
0 180
10080
11070 12060 13050 14040 15030
1602017010
1800
BO
A
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
obtuse angle
opposite rays
plane
point
postulate
ray
right angle
segment
Chapter 1 (p. 39) Chapter 1 (p. 5)
Chapter 1 (p. 4) Chapter 1 (p. 4)
Chapter 1 (p. 12) Chapter 1 (p. 5)
Chapter 1 (p. 39) Chapter 1 (p. 5)
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
If point C lies on AB
between A and B, then CA
and CB
are opposite rays.
CA CB and are opposite rays.
An angle that has a measure greater than 90 and
less than 180
A location in space that is represented by a dot and has no dimension
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
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.
AB
A rule that is accepted without proof
The Segment Addition Postulate states that if B is between A and C, then .AB BC AC
Consists of two endpoints and all the points between them
An angle that has a measure of 90
A BC
A
A
point AA
CM
B
plane M, or plane ABC
A B
endpoint
A B
endpoint endpoint
A
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
segment bisector
sides of an angle
straight angle
supplementary angles
undefined terms
vertex of an angle
vertical angles
Chapter 1 (p. 20) Chapter 1 (p. 38)
Chapter 1 (p. 39) Chapter 1 (p. 48)
Chapter 1 (p. 4) Chapter 1 (p. 38)
Chapter 1 (p. 50)
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
The rays of an angle
A point, ray, line, line segment, or plane that intersects the segment at its midpoint
CD is a segment bisector of AB.
So, AM MB AM MBand .
Two angles whose measures have a sum of 180
and JKM LKM are supplementary angles.
An angle that has a measure of 180
The common endpoint of the two rays that form an angle
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.
Two angles whose sides form two pairs of opposite rays
3 and 6 are vertical angles.
4 and 5 are vertical angles.
B
C
A
sides A MD
C
B
K L
M
J
75° 105°
A
B
C
A
vertex
46
53
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
biconditional statement
conclusion
conditional statement
conjecture
contrapositive
converse
counterexample
deductive reasoning
Chapter 2 (p. 69) Chapter 2 (p. 66)
Chapter 2 (p. 66) Chapter 2 (p. 76)
Chapter 2 (p. 67) Chapter 2 (p. 67)
Chapter 2 (p. 77) Chapter 2 (p. 78)
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
The “then” part of a conditional statement written in if-then form
If you are in Houston, then you are in Texas.
A statement that contains the phrase “if and only if”
Two lines intersect to form a right angle if and only if they are perpendicular lines.
An unproven statement that is based on observations
Conjecture: The sum of any three consecutive integers is three times the second number.
A logical statement that has a hypothesis and a conclusion
If you are in Houston, then you are in Texas.
The statement formed by exchanging the hypothesis and conclusion 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.
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.
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
You use deductive reasoning to write geometric proofs.
A specific case for which a conjecture is false
Conjecture: The sum of two numbers is always more than the greater number.
Counterexample: 2 ( 3) 5
5 2
hypothesis, p conclusion, q
hypothesis, p conclusion, q
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
equivalent statements
flowchart proof (flow proof)
hypothesis
if-then form
inductive reasoning
inverse
line perpendicular to a plane
negation
Chapter 2 (p. 67) Chapter 2 (p. 106)
Chapter 2 (p. 66) Chapter 2 (p. 66)
Chapter 2 (p. 76) Chapter 2 (p. 67)
Chapter 2 (p. 66)Chapter 2 (p. 86)
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
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
If you are in Houston, then you are in Texas.
The “if” part of a conditional statement written in if-then form
If you are in Houston, then you are in Texas.
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.
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.
The opposite of a statement
If a statement is p, then the negation is “not p,” written ~p.
Statement: The ball is red.
Negation: The ball is not red.
A line that intersects the plane in a point and is perpendicular to every line in the plane that intersects it at that point
Line t is perpendicular to plane P.
A
p
q
t
conclusion, qhypothesis, pconclusion, qhypothesis, p
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
paragraph proof
perpendicular lines
proof
theorem
truth table
truth value
two column proof
Chapter 2 (p. 108) Chapter 2 (p. 68)
Chapter 2 (p. 100) Chapter 2 (p. 101)
Chapter 2 (p. 70) Chapter 2 (p. 70)
Chapter 2 (p. 100)
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
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
A statement that can be proven
Vertical angles are congruent.
A logical argument that uses deductive reasoning to show that a statement is true
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
m
⊥m
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
alternate exterior angles
alternate interior angles
consecutive interior angles
corresponding angles
directed line segment
distance from a point to a line
parallel lines
parallel planes
Chapter 3 (p. 128) Chapter 3 (p. 128)
Chapter 3 (p. 128) Chapter 3 (p. 128)
Chapter 3 (p. 156) Chapter 3 (p. 148)
Chapter 3 (p. 126) Chapter 3 (p. 126)
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
Two angles that are formed by two lines and a transversal that are between the two lines and on opposite sides of the transversal
4 and 5 are alternate interior angles.
Two angles that are formed by two lines and a transversal that are outside the two lines and on opposite sides of the transversal
1 and 8 are alternate exterior angles.
Two angles that are formed by two lines and a transversal that are in corresponding positions
2 and 6 are corresponding 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
3 and 5 are consecutive interior angles.
The length of the perpendicular segment from the point to the line
The distance between point A and the line k is AB.
A segment that represents moving from point A to point B is called the directed line segment AB.
Planes that do not intersect
S T
Coplanar lines that do not intersect
m
45
t1
8
t
2
6
t
35
t
k
A
B
x
y
4
2
8
6
42 86
A(3, 2)
B(6, 8)
T
S m
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
perpendicular bisector
skew lines
transversal
Chapter 3 (p. 149) Chapter 3 (p. 126)
Chapter 3 (p. 128)
Vocabulary Flash Cards
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Lines that do not intersect and are not coplanar
Lines n and p are skew lines.
A line that is perpendicular to a segment at its midpoint
Line n is the perpendicular bisector of .PQ
A line that intersects two or more coplanar lines at different points.
transversal t
A
p
nM
n
QP
t
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
angle of rotation
center of dilation
center of rotation
center of symmetry
component form
composition of transformations
congruence transformation
congruent figures
Chapter 4 (p. 190) Chapter 4 (p. 208)
Chapter 4 (p. 193)Chapter 4 (p. 190)
Chapter 4 (p. 176)
Chapter 4 (p. 201) Chapter 4 (p. 200)
Chapter 4 (p. 174)
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
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
The center of rotation in a figure that has rotational symmetry
The parallelogram has rotational symmetry. The center is the intersection
of the diagonals. A 180 rotation about the center maps the parallelogram onto itself.
The fixed point in a rotation
The combination of two or more transformations to form a single transformation
A glide reflection is an example of a composition of transformations.
A form of a vector that combines the horizontal and vertical components
The component form of PQ is 4, 2 .
Geometric figures that have the same size and shape
ABC DEF
A transformation that preserves length and angle measure
Translations, reflections, and rotations are three types of congruence transformations.
QC
P
R
P′
Q′
R′center of dilation
R
Q
P
Q′
R′
40°angle ofrotation
center of rotation
R
Q
P
Q′
R′
40°angle ofrotation
center of rotation
4 units right
2 units upP
Q
horizontal component
verticalcomponent
A C
B
F D
E
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
dilation
enlargement
glide reflection
horizontal component
image
initial point
line of reflection
line symmetry
Chapter 4 (p. 208) Chapter 4 (p. 208)
Chapter 4 (p. 184) Chapter 4 (p. 174)
Chapter 4 (p. 174)Chapter 4 (p. 174)
Chapter 4 (p. 182) Chapter 4 (p. 185)
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
A dilation in which the scale factor is greater than 1
A dilation with a scale factor of 2 is an enlargement.
A transformation in which a figure is enlarged or reduced with respect to a fixed point
Scale factor of dilation is .CP
CP
The horizontal change from the starting point of a vector to the ending point
A transformation involving a translation followed by a reflection
The starting point of a vector
Point J is the initial point of .JK
A figure that results from the transformation of a geometric figure
A B C D is the image of ABCD after a translation.
A figure in the plane has line symmetry when the figure can be mapped onto itself by a reflection in a line.
Two lines of symmetry
A line that acts as a mirror for a reflection
A B C is the image of ABC after a reflection in the line m.
QC
P
R
P′
Q′
R′center of dilation
4 units rightP
Q
horizontal component
P
P′
P″
Q′ Q″
Q
k
J
K
x
y
4
6
42 6
BC
A DA′
B′C′
D′
AB
m
x
y4
2
6
A′
B′C
C′
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
line of symmetry
preimage
reduction
reflection
rigid motion
rotation
rotational symmetry
scale factor
Chapter 4 (p. 208) Chapter 4 (p. 182)
Chapter 4 (p. 176) Chapter 4 (p. 190)
Chapter 4 (p. 193) Chapter 4 (p. 208)
Chapter 4 (p. 174)Chapter 4 (p. 185)
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
The original figure before a transformation
ABCD is the preimage and A B C D is the image after a translation.
A line of reflection that maps a figure onto itself
Two lines of symmetry
A transformation that uses a line like a mirror to reflect a figure
A B C is the image of ABC after a reflection
in the line m.
A dilation in which the scale factor is greater than 0 and less than 1
A dilation with a scale factor of 1
2 is a reduction.
A transformation in which a figure is turned about a fixed point
A transformation that preserves length and angle measure
Translations, reflections, and rotations are three types of rigid motions.
The ratio of the lengths of the corresponding sides of the image and the preimage of a dilation
Scale factor of dilation is .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.
x
y
4
6
42 6
BC
A DA′
B′C′
D′
AB
m
x
y4
2
6
A′
B′C
C′
R
Q
P
Q′
R′
40°angle ofrotation
center ofrotation
QC
P
R
P′
Q′
R′center of dilation
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
similar figures
similarity transformation
terminal point
transformation
translation
vector
vertical component
Chapter 4 (p. 216) Chapter 4 (p. 216)
Chapter 4 (p. 174) Chapter 4 (p. 174)
Chapter 4 (p. 174) Chapter 4 (p. 174)
Chapter 4 (p. 174)
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
A dilation or a composition of rigid motions and dilations
A B C is the image of ABC after a
similarity transformation.
Geometric figures that have the same shape, but not necessarily the same size
Trapezoid PQRS is similar to trapezoid WXYZ.
A function that moves or changes a figure in some way to produce a new figure
Four basic transformations are translations, reflections, rotations, and dilations.
The ending point of a vector
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
JK
with initial point J and terminal point K.
A transformation that moves every point of a figure the same distance in the same direction
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
x
y
4
2
6
42 86−2−4
B(−2, 2)A(−4, 1)
C(−2, 1)C′(3, 2)A′(1, 2)
B′(3, 3)
A″(2, 4)B″(6, 6)
C″(6, 4)
x
y
2
4 6−2−4
P Q
S R
W
ZY
X
J
K
J
K
x
y
3
42 86
BC
AA′
B′C′
2 units up
P
Qverticalcomponent
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
base angles of an isosceles triangle
base of an isosceles triangle
coordinate proof
corollary to a theorem
corresponding parts
exterior angles
hypotenuse
interior angles
Chapter 5 (p. 284) Chapter 5 (p. 235)
Chapter 5 (p. 240) Chapter 5 (p. 233)
Chapter 5 (p. 264) Chapter 5 (p. 233)
Chapter 5 (p. 252)Chapter 5 (p. 252)
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
The side of an isosceles triangle that is not one of the legs
The two angles adjacent to the base of an isosceles triangle
A statement that can be proved easily using the theorem
The Corollary to the Triangle Sum Theorem states that the acute angles of a right triangle are complementary.
A style of proof that involves placing geometric figures in a coordinate plane
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
Corresponding angles , , A E C FBD
Corresponding sides
, , C FB E FA ED DB AC
Angles of a polygon
The side opposite the right angle of a right triangle
base
leg leg
baseangles
base
leg leg
A
B
C
exterior angles
A
B
C
interior angles
hypotenuse
A
B
C
D
E
F
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
legs of an isosceles triangle
legs of a right triangle
vertex angle
Chapter 5 (p. 252)
Chapter 5 (p. 252) Chapter 5 (p. 264)
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
The sides adjacent to the right angle of a right triangle
The two congruent sides of an isosceles triangle
The angle formed by the legs of an isosceles triangle
leg
legleg leg
vertex angle
base
leg leg
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
altitude of a triangle
centroid
circumcenter
concurrent
equidistant
incenter
indirect proof
median of a triangle
Chapter 6 (p. 321) Chapter 6 (p. 320)
Chapter 6 (p. 310) Chapter 6 (p. 310)
Chapter 6 (p. 302) Chapter 6 (p. 313)
Chapter 6 (p. 336) Chapter 6 (p. 320)
Vocabulary Flash Cards
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The point of concurrency of the three medians of a triangle
P is the centroid of ABC.
The perpendicular segment from a vertex of a triangle to the opposite side or to the line that contains the opposite side
Three or more lines, rays, or segments that intersect in the same point
Lines j, k, and are concurrent.
The point of concurrency of the three perpendicular bisectors of a triangle
P is the circumcenter of ABC.
The point of concurrency of the angle bisectors of a triangle
P is the incenter of ABC.
A point is equidistant from two figures when it is the same distance from each figure.
X is equidistant from Y and Z.
A segment from a vertex of a triangle to the midpoint of the opposite side
BD is a median of ABC.
A style of proof in which you temporarily assume that the desired conclusion is false, then reason logically to a contradiction
This proves that the original statement is true.
A F C
E
B
DP
Q
P R
Q
P R
altitude fromQ to PR
P
j
k
A C
B
P
A C
B
P
Y
XZ
A D C
B
Vocabulary Flash Cards
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midsegment of a triangle
orthocenter
point of concurrency
Chapter 6 (p. 330) Chapter 6 (p. 321)
Chapter 6 (p. 310)
Vocabulary Flash Cards
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The point of concurrency of the lines containing the altitudes of a triangle
G is the orthocenter of ABC.
A segment that connects the midpoints of two sides of a triangle
The midsegments of ABC are MP, MN,
and NP.
The point of intersection of concurrent lines, rays, or segments
P is the point of concurrency for lines j, k, and .
BFC
AE
G
D
A C
P
N
M
B
Pk
j
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
base angles of a trapezoid
bases of a trapezoid
diagonal
equiangular polygon
equilateral polygon
isosceles trapezoid
kite
legs of a trapezoid
Chapter 7 (p. 398) Chapter 7 (p. 398)
Chapter 7 (p. 360) Chapter 7 (p. 361)
Chapter 7 (p. 401) Chapter 7 (p. 398)
Chapter 7 (p. 361) Chapter 7 (p. 398)
Vocabulary Flash Cards
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The parallel sides of a trapezoid
Either pair of consecutive angles whose common side is a base of a trapezoid
A polygon in which all angles are congruent
A segment that joins two nonconsecutive vertices of a polygon
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
C
DA
B base
base
C
DA
B base
base
base angles
base angles
D
EA
B
C
diagonals
C
DA
B
legleg
Vocabulary Flash Cards
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midsegment of a trapezoid
parallelogram
rectangle
regular polygon
rhombus
square
trapezoid
Chapter 7 (p. 388) Chapter 7 (p. 361)
Chapter 7 (p. 368)Chapter 7 (p. 400)
Chapter 7 (p. 388) Chapter 7 (p. 388)
Chapter 7 (p. 398)
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
A quadrilateral with both pairs of opposite sides parallel
PQRS
The segment that connects the midpoints of the legs of a trapezoid
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
P
Q R
S
midsegment
C
DA
B base
base
legleg
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
angle of depression
angle of elevation
cosine
geometric mean
inverse cosine
inverse sine
inverse tangent
Law of Cosines
Chapter 9 (p. 490)
Chapter 9 (p. 494) Chapter 9 (p. 480)
Chapter 9 (p. 502) Chapter 9 (p. 502)
Chapter 9 (p. 502) Chapter 9 (p. 511)
Chapter 9 (p. 497)
Vocabulary Flash Cards
Copyright © Big Ideas Learning, LLC Big Ideas Math Geometry All rights reserved.
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
The positive number x that satisfies a x
x b
So, 2x ab and .x ab
The geometric mean of 4 and 16 is 4 16, or 8.
A trigonometric ratio for acute angles that involves the lengths of a leg and the hypotenuse of a right triangle
length of leg adjacent to
coslength of hypotenuse
CA
AB
A A
An inverse trigonometric ratio, abbreviated as 1sin
For acute angle A, if sin ,A y then 1sin .y m A
BC
m AAB
1sin
An inverse trigonometric ratio, abbreviated as 1cos
For acute angle A, if cos ,A z then 1cos .z m A
AC
m AAB
1cos
For ABC with side lengths of a, b, and c, 2 2 2
2 2 2
2 2 2
2 cos ,
2 cos , and
2 cos .
a b c bc A
b a c ac B
c a b ab C
An inverse trigonometric ratio, abbreviated as 1tan
For acute angle A, if tan ,A x then 1tan .x m A
BC
m AAC
1tan
angle of elevation
angle of depression
AC
Bhypotenuse
leg adjacentto ∠A
legopposite
∠A
C
B
AC
B
A
C
B
A
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Law of Sines
Pythagorean triple
sine
solve a right triangle
standard position
tangent
trigonometric ratio
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Chapter 9 (p. 488)
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A set of three positive integers a, b, and c that
satisfy the equation 2 2 2c a b
Common Pythagorean triples:
3, 4, 5
5, 12, 13
8, 15, 17
7, 24, 25
For ABC with side lengths of a, b, and c,
sin sin sin and
.sin sin sin
A B C
a b ca b c
A B C
To find all unknown side lengths and angle measures of a right triangle
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
A trigonometric ratio for acute angles that involves the lengths of a leg and the hypotenuse of a right triangle
length of leg opposite
sinlength of hypotenuse
CA
AB
A B
A trigonometric ratio for acute angles that involves the lengths of the legs of a right triangle
length of leg opposite
tanlength of leg adjacent to
AA
A C
BC
A
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.
A ratio of the lengths of two sides in a right triangle
Three common trigonometric ratios are sine, cosine, and tangent.
BCA
ACBC
AABAC
AAB
3tan
43
sin 54
cos 5
AC
Bhypotenuse
leg adjacentto ∠A
legopposite
∠A
AC
Bhypotenuse
leg adjacentto ∠A
legopposite
∠A
x
y
0.5
−0.5
0.5−0.5 CA
B
4
53
A
B
C
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adjacent arcs
center of a circle
central angle of a circle
chord of a circle
circle
circumscribed angle
circumscribed circle
common tangent
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The point from which all points on a circle are equidistant
circle with center P, or P
Arcs of a circle that have exactly one point in common
and AB BC are adjacent arcs.
A segment whose endpoints are on a circle
An angle whose vertex is the center of a circle
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
circle with center P, or P
A line or segment that is tangent to two coplanar circles
A circle that contains all the vertices of an inscribed polygon
P B
C
A
TS
RP
Qchords
C
P
Q
A
C
B
circumscribedangle
P
circumscribedcircle
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concentric circles
congruent arcs
congruent circles
diameter
external segment
inscribed angle
inscribed polygon
intercepted arc
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Arcs that have the same measure and arc of the same circle or of congruent circles
CD EF
Coplanar circles that have a common center
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
P Q
An angle whose vertex is on a circle and whose sides contain chords of the circle
The part of a secant segment that is outside the circle
An arc that lies between two lines, rays, or segments
A polygon in which all of the vertices lie on a circle
C FB
D E
80°80°
diameter
P4 m
4 m
Q
A
C
Binscribedangle
RQ
P
external segment
S
secant segment
PR is a secant segment.PQ is the external segment of PR.
A
C
B interceptedarc
inscribedpolygon
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major arc
measure of a major arc
measure of a minor arc
minor arc
point of tangency
radius of a circle
secant
secant segment
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The measure of a major arc’s central angle
mADB 360 50 310
An arc with a measure greater than 180
An arc with a measure less than 180
The measure of a minor arc’s central angle
A segment whose endpoints are the center and any point on a circle
The point at which a tangent line intersects a circle
A segment that contains a chord of a circle, and has exactly one endpoint outside the circle
A line that intersects a circle in two points
50°
A
BC
D
major arc ADB
A
BC
D
minor arc AB
A
BC
D
50°mAB = 50°
A
BC
D
Q
Pradius point of
tangency
tangent AB
RQ
P
S
secant segment
secant
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segments of a chord
semicircle
similar arcs
standard equation of a circle
subtend
tangent of a circle
tangent circles
tangent segment
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An arc with endpoints that are the endpoints of a diameter
QSR is a semicircle.
The segments formed from two chords that intersect in the interior of a circle
EA EBand are segments of chord AB DE,
ECand are segments of chord DC.
2 2 2( ) ( ) ,x h y k r where r is the radius
and ( , )h k is the center
The standard equation of a circle with center (2, 3)
and radius 4 is 2 2( 2) ( 3) 16.x y
Arcs that have the same measure
~RS TU
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.
AC B
AC B
subtends .
subtends .
A segment that is tangent to a circle at an endpoint
Coplanar circles that intersect in one point
PQ R
S
DB
C
EA
Q S U
R
T
point oftangency
tangent AB
A
C
B interceptedarc
inscribedangle
RQ
P
tangent segment S
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apothem of a regular polygon
arc length
axis of revolution
Cavalieri’s Principle
center of a regular polygon
central angle of a regular polygon
chord of a sphere
circumference
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A portion of the circumference of a circle
Arc length of , or
2 360
Arc length of 2360
AB mAB
mABA
r
B r
The distance from the center to any side of a regular polygon
If two solids have the same height and the same cross-sectional area at every level, then they have the same volume.
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.
The line around which a two-dimensional shape is rotated to form a three-dimensional figure
An angle formed by two radii drawn to consecutive vertices of a polygon
MPN is a central angle.
The center of a polygon’s circumscribed circle
The distance around a circle
A segment whose endpoints are on a sphere
apothem
B B h
P
M
N
P
center
r
dC
C = d = 2 rπ π
chord
rP
A
B
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cross section
density
edge
face
great circle
lateral surface of a cone
net
polyhedron
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The amount of matter that an object has in a given unit of volume
massdensity
volume
The intersection of a plane and a solid
A flat surface of a polyhedron
A line segment formed by the intersection of two faces of a polyhedron
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
A solid that is bounded by polygons
A two-dimensional pattern that can be folded to form a three-dimensional figure
cross section
plane
face
edge
lateral surface
base
greatcircle
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population density
radian
radius of a regular polygon
sector of a circle
similar solids
solid of revolution
vertex of a polyhedron
volume
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A unit of measurement for angles
45 radians4
A measure of how many people live within a given area
number of peoplepopulation density
area of land
The region bounded by two radii of the circle and their intercepted arc
sector APB
The radius of a polygon’s circumscribed circle
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
3Volume 3(4)(6) 72ft
A point of a polyhedron where three or more edges meet
rB
A
PP
N
radius
3 ft
4 ft6 ft
vertex
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