Download Geometry Vocabulary

Geometry Vocabulary
Word
Definition
Examples
Acute angle
An angle that measures between 0
and 90 degrees
0° < x < 90°
Acute triangle
All angles in the triangle are acute
A 40 - 60 - 80 triangle is
acute
Adjacent
angles
Two coplanar angles with a common side, a common vertex, and no
common interior points
Adjacent arcs
Two arcs in the same circle that have exactly one point in common.
Two non-adjacent angles that lie on the opposite sides of a
transversal between two lines that the transversal intersects (a
Alternate
description of the location of the angles); alternate interior angles
interior angles are congruent if the lines intersected by the transversal are
parallel.
Angle
The shape formed by two rays (called sides of the angle) with the
same endpoint (called the vertex of the angle). In geometry an
angle can be defined by the vertex or by the rays and vertex.
Angle bisector A ray that divides an angle into two congruent (equal) angles
Exactly half the circle is called a semicircle.
Less than half is a minor arc and more than half is a
major arc.
Arc
Part of a
circle
Arc length
The length in linear measure of an arc of a circle; the product of
the ratio of the arc measure and 360º and the circumference of
the circle
Angle of
Depression
The angle between the
An angle from the horizontal down to
viewer and something below
a line of sight
them
Angle of
Elevation
An angle from the horizontal up to a
line of sight
Bisector (of a
line segment)
A line, segment, ray, or plane that intersects a segment at its
midpoint
The angle between the
ground and something above
the ground
Bisector (of an
A line or ray that divides the angle into two congruent angles.
angle)
Central angle
An angle whose vertex is the center of a circle
Centroid
The point in a triangle where the medians of the triangle intersect.
Chord
A line segment whose endpoints lie on the circle.
If a chord goes through the center of a circle, it is a diameter.
Circle
The set of all points in a plane that
are a constant distance of r from a
given point called the center. If the
center is at (h,k) and the radius is r,
the equation of the circle is (x-h)2 +
(y-k)2 = r2
Circle Graph
A graph that represents the frequency of data as slices of a
circle. The size of each slice represents the frequency, usually
recorded as a percent.
Circumcenter
The point in a triangle where the perpendicular bisectors of the
sides of the triangle intersect.
Collinear
Points that lie on the same line
Compass
A tool used to draw circles and parts of circles
Complementary Two positive angles whose measures
angles
add to 90 degrees
(x-2)2 + (y-3)2 = 52 is a
circle with center at (2,3)
and a radius of 5
Points that all line up
A + B = 90°
Concave
polygon
When a diagonal contains points outside the polygon.
Conditional
statement
A statement that can be written in the form “If p, then q.” p is
the hypothesis and q is the conclusion. Symbolically, if p, then q
can be written as p→q.
Congruent
Objects that are the same size and the same shape. The symbol
for congruent is an equal sign with a squiggle over it.
Conjecture
The conclusion reached in a math statement based on reasoning
Construction
Using only a compass and a straight edge to draw a
geometric figure.
Contrapositive
In the contrapositive of a conditional statement, the
hypothesis and conclusion are both reversed and
negated. “If p, then q.” becomes “If not q, then not p.”.
The contrapositve has the same truth value as the
original statement.
Converse
In the converse of a conditional statement, the
hypothesis and conclusion are reversed. “If p, then q.”
becomes “If q, then p.”.
Convex polygon
No diagonal contains points outside the polygon
Coplanar
Points and lines that are in the same plane
Corresponding angles
(parallel lines)
Two angles that lie on the same side of a transversal,
in corresponding positions with respect to the two
lines that the transversal intersects.
Corresponding angles
(in polygons)
Angles that are in the same position in different plane
figures
Corresponding parts
Matching sides and angles in a polygon.
Corollary
A statement that follows directly from a theorem.
Cosine
The ratio of the length of the side side adjacent
adjacent to an angle and the
divided by
hypotenuse in a right triangle
hypotenuse
Deductive reasoning
A method of reasoning logically from given facts, rules,
definitions, or properties to a conclusion.
Diameter
In a circle, any segment that contains the center of
the circle and has both endpoints on the circle.
Dilation
A transformation in which a figure is made larger or
smaller, but not moved.
Distance Formula
Using the Pythagorean Theorem to find the distance
between two points on a coordinate grid)
Equiangular polygon
A polygon where all the angles are
congruent
Equiangular triangle
A triangle where all the angles are
All angles equal
congruent
Equilateral polygon
A polygon where all the sides are
congruent
All sides equal
Equilateral triangle
A triangle where all the sides are
congruent
All sides equal
Euclidean geometry
A geometric system based on the five postulates of
Euclid
1. A straight line can be drawn joining any two points.
2. Any straight line segment can be extended
indefinitely in a straight line.
3. Given any straight line segment, a circle can be
drawn having the segment as radius and one endpoint
as center.
All angles equal
4. All right angles are congruent.
5. If two lines are drawn which intersect a third in
such a way that the sum of the inner angles on one side
is less than two right angles, then the two lines
inevitably must intersect each other on that side if
extended far enough. This postulate is equivalent to
what is known as the parallel postulate (the parallel
postulate)
Euler Line
In geometry, the centroid, circumcenter and
orthocenter of any triangle always lie on a straight
line, called the Euler line.
Exterior angle
In a polygon, the angle formed by a side and an
extension of a side.
Foundation drawing
Drawing that shows the base of an object (its
foundation) and the height of each part.
Geometric Mean
The geometric mean of two numbers a and b is the
square root of a times b
Geometry
The study of lines, shapes, measurements, angles, and
figures in space based on defined properties.
Plane geometry studies shapes on flat surfaces, like
your paper or the chalkboard. Spherical geometry
studies shapes on a sphere, like a ball or the earth.
Hypotenuse
In a right triangle, the side
opposite the right angle - the
longest side in a right triangle
Hypothesis
In a conditional statement (if _
then_), the statement that
immediately follows the if.
If and only if
(conditional statements)
In an equivalence statement, the words if and only if
may be represented by the short symbol iff. Then the
definition of an equivalence statement is written as
follows:
p iff q = (p implies q) and (q implies p).
Here the first implication means that when p is true, q
must be true, and we cannot have p true and q false.
The second implication means that when q is true, p
must be true, and we cannot have q true and p false.
Therefore, in an equivalence statement the only
The assumption you
start with
possibilities are: (1) p and q both true, and (2) p and q
both false. Then p and q are said to be equivalent.
Image
The position of a figure after a transformation.
Incenter
The point in a triangle where the angle bisectors of
the triangle intersect.
For the pattern 2,
4, 6, 8 you can
induce that since
they are all even
numbers, the next
number must be 10
Inductive Reasoning
A method used to reach
conclusions based on an observed
pattern.
Intersect
Lines intersect when they cross. The point where they
cross is called the intersection.
Isometric drawing
The drawing of a three-dimensional object that shows
the corners.
Isosceles trapezoid
A trapezoid whose nonparallel
sides are congruent.
The top and bottom are
parallel, the sides are the
same size, and the diagonals
are equal.
Isosceles triangle
A triangle where at least two
sides are congruent
Kite
A quadrilateral with two pairs
of adjacent sides congruent
and no opposite sides
congruent
Law of Detachment
Suppose that the statements p and p implies q are
both true. Then we may write: p and (p implies q).
By the definition of the implication, this is: p and (notp or q).
By the distributive law, we now have: (p and not-p) or
(p and q).
By the law of contradiction p and not-p is false, so p
and q must be true. This shows we may conclude that q
is true, because we have already supposed that p is
Two or more sides
equal
true.
We may summarize this result as follows: From p and
(p implies q) we conclude q.
Law of Syllogism
Suppose the statements p implies q and q implies r are
both true. Then we may write:
(p implies q) and (q implies r).
The first implication means that when p is true, q must
also be true and we cannot have p true and q false. The
second implication means that when q is true r must
also be true, and we cannot have q true and r false.
These results show that when p is true r must also be
true, and we cannot have p true and r false. In other
words: p implies r.
We may summarize this result as follows:
From (p implies q) and (q implies r) we conclude (p
implies r).
Legs of a right triangle
The sides that form the right
angle in a right triangle
Line
A series of points that extends forever in two
directions. A line is uniquely defined if you know two
points on the line.
Line segment
Part of a line consisting of two endpoints and all the
points between them.
Linear pair
two adjacent angles whose non-common sides are
opposite rays; the sum of the measures of the angles
in a linear pair is 180 º
<1 and <2 comprise a linear pair.
Median
geometry
In a triangle, a line drawn from the midpoint of a side
to the vertex opposite. Every triangle has three
medians.
Midpoint
The point that divides a line into
two equal pieces. For the line
with end points at A(x1,y1) and
B(x2,y2), the midpoint is located
at:
x1 + x2 y1 + y2
,
2
2
The midpoint of a
line with ends at
(2,5) and (4,7) is at
(3,6)
Negation
The opposite of a
statement:
If a statement is represented by
p - Today is Monday
p, then the negation is not p.
not p - Today is not
Monday.
A polygon with 5
sides is a pentagon
A polygon with 42
sides is a 42-gon
N-gon
A polygon with n sides.
Oblique triangle
Any triangle that is not a right triangle
Obtuse angle
An angle that
measures between 90
and 180 degrees
Obtuse triangle
A triangle with one
obtuse angle
Opposite rays
Two collinear rays that share the same endpoint and
together form a straight line
Orthocenter
The point in a triangle where the altitudes of the
triangle intersect.
Orthographic drawing
A drawing that represents a three dimensional object
by showing separate drawings for the front, top and
right side views
Parallel lines
Lines that
are always
the same
distance
apart, they
never cross.
Parallelogram
A
quadrilateral
where the
Rectangles, squares, and diamonds are
opposite
parallelograms
sides are
parallel
Pascal's Triangle
A pattern for
finding the
coefficients
of the terms
90° < x < 180°
One angle bigger than 90°
Lines that
y = 3x + 1 and y = 3x - 5 are
have the
parallel because they both
same
have slope = 3
slope
1
1 1
1 2 1
1 3 3 1
in a binomial
expansion. It
is also used in
probability.
Perpendicular bisector
A line,
segment, or
ray that is
perpendicular
to the
original
segment at
its midpoint
Perpendicular lines
Lines that
cross at right
angles. The
product of
the slopes is
-1.
Perspective drawing
Drawing that makes a two-dimensional image look like a
three-dimensional object
Pi Π π
Most frequently used Greek letter, it represents the
ratio of diameter to circumference in math problems
about circles. It also represents an angle measure in
radians equal to 180°
Plane
A flat surface that extends forever in all directions.
Planes have no thickness. Usually drawn as a shaded
parallelogram.
Platonic solids
The five regular polyhedra: tetrahedron, hexahedron,
octahedron, dodecahedron, or icosahedron
Point
A location in space that has no size. Any point can be
uniquely identified by a set of coordinates (x, y).
Polygon
A closed plane figure
with at least three
sides
Postulate
An accepted statement "Two points define exactly one
of fact that can be
straight line" is a postulate
y = 2x + 1 and y = -½x - 5 are
perpendicular because 2 • (-½) = -1
A triangle is a 3-sided polygon
used to prove
theorems
Pre-Image
The position of a figure before a transformation
Proof
A valid argument in which all of the premises are true
Protractor
A device used to measure the size of an angle in
degrees.
Pythagorean theorem
In a right triangle, the sum of
the squares of the lengths of
the two sides (legs a and b) is
equal to the square of the
length of the hypotenuse (c).
a2 + b2 = c2
Quadrilateral
A geometric figure with four
sides and four angles
A rectangle is
quadrilateral
Radius
In a circle, any segment that has one endpoint at the
center of the circle and the other endpoint on the
circle
Ray
The part of a line consisting of one endpoint and all the
points extending forever in one direction
Rectangle
A parallelogram with four right angles
Regular polygon
A polygon that is both equilateral and equiangular.
For each exterior angle of a triangle, the two non-
Remote interior angles
adjacent angles
Rhombus
A parallelogram with
A diamond is a rhombus
four congruent sides
Right Angle
An angle that
measures 90°
Right Triangle
A triangle that has one 90° angle. The other two angles
will add up to 90°
Same-side interior angles
Two angles that lie on the same side of a transversal
and between the lines cut by the transversal, in
corresponding positions with respect to the two lines
that the transversal intersects.
x = 90°
Scalar
A quantity that represents a magnitude. It can be
represented by a real number.
Scale
Scale is the ratio of any length in a scale drawing to
the corresponding actual length; the lengths may be in
different units
Scalene triangle
A triangle
with no
sides
congruent
Secant
A line, ray, or segment that intersects a circle at two
points (i.e. that contains a chord). A secant to a sphere
is a line, ray, or segment that intersects a sphere at
two points.
Sector of a circle
The portion of the interior of a
circle intercepted by a central
angle.
Segment
Part of a line consisting of two endpoints and all the
points between them
Semicircle
Exactly half a circle
Similar Figures
Figures that have the same
shape, but not the same size.
Same angles,
proportional sides
Similar Triangles
Triangles that have the same
angles, but not necessarily the
same size.
Same shape
Similarity ratio
The ratio of the lengths of corresponding sides in a
similar polygon.
Sine
The ratio of the length of the
side opposite an angle and the
hypotenuse in a right triangle
Skew lines
Two lines that are not in the same plane. They do not
intersect and they are not parallel.
Space
The set of all points.
Square
A parallelogram with four
All sides and angles
congruent sides and four right
equal
angles
Straight angle
An angle that measures 180°,
a straight line.
All sides are a
different length
Like a slice of a
round pie
side opposite divided
by hypotenuse
x = 180°
Straightedge
A ruler that doesn't have any markings on it used to
draw lines where the exact length doesn't matter.
Supplementary angles
Two positive angles whose
measures add to 180 degrees.
When adjacent (sharing a side)
supplementary angles make a
straight line.
Tangent
(to a circle)
A line that intersects a circle in exactly one point.
The ratio of the length of the
Tangent
side opposite an angle and the
(trigonometric function) side adjacent to the angle in a
right triangle.
A + B = 180°
side opposite
divided by side
adjacent
Theorem
A conjecture that is proven. In geometry, properties,
postulates and theorems are used to prove other
theorems
Transversal
A line that intersects two or more other lines in the
same plane at different points.
Trapezoid
A quadrilateral with exactly one
pair of parallel sides.
Triangle
A polygon with three sides and three angles
Undefined terms
Words, usually easily understood,
that are not formally explained or
defined.
Vertex
The point on a triangle where the
sides come together. The vertices
of triangles are usually labeled with
capital letters.
Two sides are
parallel, other
sides are not.
In geometry,
point, line, and
plane are
undefined terms
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Vertical angles
Two angles whose sides are opposite rays
Volume
The measure of the amount of
space enclosed by a threedimensional figure.
The volume of a
cube is side X
side X side