# New York State Education Department Elementary, Secondary, and Continuing Education Suggested List of Mathematical Language All Math Words Encyclopedia Cross Reference

This list is taken from http://www.emsc.nysed.gov/3-8/LanguageGeometry.pdf.

## Geometry

### Problem Solving

AA triangle similarity
AAA triangle similarity see AA Similarity
AAS triangle congruence
additive property of equality
algorithm
apply
ASA triangle congruence
conjecture
constraints
construct
discover
dynamic geometry software see Interactive Geometry Software
explore
generalization
inductive reasoning
justify
parameters
reason
truth value
valid argument

### Reasoning and Proof

AA triangle similarity
AAA triangle similarity
AAS triangle congruence
analytical proof
angle addition postulate see Angle
ASA triangle congruence
axiom
biconditional
conclusion
conditional statement
conjecture
conjunction
contrapositive of a statement see Contraposition
converse of a statement
counterexample
deductive proof see Deduction
deductive reasoning see Deduction
definition
disjunction
dynamic geometry software see Interactive Geometry Software
equivalence relation
Euclidean Parallel Postulate see Parallel Postulate
explain
geometry
hypotenuse and leg triangle congruence
hypothesis
indirect proof see Contradiction
inductive reasoning
inverse of a statement
Investigate
justify
logical equivalent
negation
paragraph proof
parallel postulate(s)
proof
proportional
Pythagorean Theorem
reason
reflexive property of equality
SAS triangle congruence
SAS Similarity Theorem see SAS Congruence
SSS triangle congruence
substitution property
subtraction property of equality see Equal
symmetric property of equality see Equal
theorem
transformational proof
transitive property of equality see Equal
truth value
two-column proof
undefined terms
union of sets
valid argument

### Communication

axiom
biconditional
compound statement
conclusion
conditional statement
conjecture
conjunction
contrapositive of a statement see Contraposition
converse of a statement see Contraposition
definition
disjunction
explain
hypothesis
inverse of a statement see Contraposition
justify
negation
theorem
truth value
undefined terms

### Connections

apply
compound locus see Locus
discover

investigate
spatial relationships
union of sets

### Representation

analytical geometry
coordinate geometry see Analytic Geometry
definition
Euclidean geometry
function
graphical representation see Represent
locus of points see Locus
logical equivalence
non-Euclidean geometry see Euclidean Geometry

transformational geometry
two dimensional space see Space

### Geometric Relationships

AA triangle similarity
AAA triangle similarity see AA Similarity
AAS triangle congruence
ASA triangle congruence
absolute value
acute angle see Angle
acute triangle see Triangle
algebraic representation see Algebraic
alternate interior angles see Alternate Angles

analytic geometry
angle
angle bisector see Angle
angle measure see Angle
apothem
arc
arc measure see Arc
area
axis of symmetry see Axis
base
betweeness
bisector
center of a circle
center of a regular polygon see Regular Polygon
center of gravity see Center
central angle see Angle
central angle of a regular polygon see Regular Polygon
centroid see Triangle
chord see Circle
circle
circumcenter
circumcircle (about a polygon) see Regular Polygon
circumference see Circle
collinear points
common tangents
complementary angles see Angle
concave polygon
concentric circles
concurrent lines see Concurrent
cone
congruence
conic sections
constant of proportionality see Constant of Variation
convex polygon
coordinate geometry see Analytic Geometry
coplanar
corresponding angles see Corresponding
corresponding parts see Corresponding
corresponding sides see Corresponding
crosssection
cube
cylinder
definition
diagonals
diameter see Circle
dihedral angle
distance see Distance
distance between a point and a line see Distance
distance between two parallel lines see Distance
distance between two points see Distance
dodecahedron
ellipse
endpoint see Line
equiangular see Angle
equidistant
equilateral triangle
equilateral polygon see Equilateral
Euclidean Geometry
Euclidean Parallel Postulate
exterior
exterior angle
external secant segment
face of a polyhedron see Polyhedron
foot of an altitude see Altitude
function
geometric mean
geometry
golden ratio see Golden Section
golden rectangle see Golden Section
great circle see Sphere
hemisphere see Sphere
Heron's formula see Triangle
hexagon
hypotenuse
icosahedron
incenter of a polygon see Regular Polygon
inclination
inscribed angle see Angle
inscribed circle
intercepted arc
intercepts
interior
intersecting line see Line
isosceles trapezoid
isosceles triangle
kite
lateral area of a prism
lateral edge
lateral face
lateral surface
legs of a right triangle see Right Triangle
legs of an isosceles trapezoid
length
line

linear pair
locus of points see Locus
major arc see Arc
mean proportional
measure of an angle see Angle
measure of an arc see Arc
median of a trapezoid

midpoint
midsegment
minor arc see Arc
n-gon see Polygon
non-collinear see Collinear
non-coplanar see Coplanar
non-Euclidean geometry see Euclidean Geometry
obtuse angle see Angle
obtuse triangle see Triangle
octagon
octahedron
opposite rays see Line
orthocenter
orthogonal
parabola
parallel line segments see Line
parallel lines see Line
parallelepiped
parallelogram
pentagon
perimeter
perpendicular bisector
perpendicular bisector concurrence
perpendicular lines see Line
perpendicular planes
Pi
Plane
Point
point of concurrency see Concurrent
point of tangency see Circle
polygon
polyhedron
prism
product property of proportions
proportional
pyramid
Pythagorean Theorem
ratio
ray see Line
real numbers
rectangle
rectangular solid
regular polygon
remote interior angles
rhombus
right angle
right triangle
scalene triangle see Triangle
secant
segment
segment of a circle see Circle
semicircle see Arc
set
similar polygons
similar triangles
skew lines see Line
slant height
slope
sphere
square
supplementary angles see Angle
surface area see Area
tangent segment see Circle
tangent to a circle see Circle
tessellation
tetrahedron
three dimensional space
topology
transformational geometry
transversal see Parallel
trapezoid
triangle
triangle inequality
trigonometry of the right triangle
two-dimensional space
vector
vertex
vertical angles
vertical line see Line
volume
x-axis see Axis
x-intercept

y-intercept

### Constructions

angle bisector see Angle
bisector
center of a regular polygon see Regular Polygon
center of gravity see Center
circumcircle (about a polygon) see Regular Polygon
compass
construct
dynamic geometry software see Interactive Geometry Software
perpendicular bisector
perpendicular bisector concurrence
perpendicular lines see Line
straightedge

### Locus

circle
compound locus see Locus
ellipse
hyperbola
locus of points see Locus
parabola

### Formal and Informal Proofs

AA triangle similarity
AAA triangle similarity see AA Similarity
AAS triangle congruence
ASA triangle congruence
angle addition postulate see Angle
axiom
biconditional
conclusion
conditional statement
conjecture
conjunction
contrapositive of a statement
converse of a statement see Contraposition
counterexample
deductive reasoning see Deduction
definition
disjunction
dynamic geometry software see Interactive Geometry Software
equivalence relation
Euclidean Parallel Postulate see Parallel Postulate
hypotenuse and leg triangle congruence
indirect proof see Contradiction
inductive reasoning
inverse of a statement see Contraposition
justify
logical equivalent
negation
parallel postulate(s)
postulate see Axiom
proof
Pythagorean Theorem
reason
reflexive property of equality
SAS triangle congruence
SAS Similarity Theorem
SSS triangle congruence
substitution property
subtraction property of equality see Equal
symmetric property of equality see Equal
theorem
transitive property of equality see Equal
transformational proof
truth value
two-column proof
undefined terms see Undefined
union of sets
valid argument

### Transformational Geometry

axis of symmetry see Axis
center of a dilation see Dilation
center of rotation see Rotation
clockwise (orientation)
composition see Composite Function
constant of proportionality
contraction see Dilation
counterclockwise (orientation) see Clockwise
dilation
direct transformation
domain
dynamic geometry software see Interactive Geometry Software
fixed point see Point
function
function notation for transformations
glide reflection
group
half-turn
Identity
image
inverse of a transformation
isometry
mapping (function)
opposite transformation
orientation
preimage
reflection
rotation

symmetry
tessellation
transformation
transformational geometry
translation

### Coordinate Geometry

abscissa see Ordered Pair
analytic geometry
Analytical Proof
Cartesian coordinates see Coordinate System
Cartesian plane see Coordinate System
center-radius equation of circle see Circle
coordinate see Coordinate System
coordinate geometry see Analytic Geometry
coordinate plane see Coordinate System
distance between two points see Distance
origin

rectangular coordinates see Coordinate System
slope-intercept equation of a line see Line
three-dimensional space see Space
two-dimensional space see Space
vector
x-axis see Axis
x-intercept
y-axis see Axis
y-intercept
z-axis see Axis

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