Download Geometry Definitions

non-coplanar - Points that are not coplanar.
oblique cone - Axis is not perpendicular to the base.
oblique cylinder - Axis not perpendicular to the bases.
oblique prism - Lateral edges not perpendicular to the planes of
the bases.
obtuse angle - Angle whose measure is between 90 and 180.
obtuse triangle - Triangle with one obtuse angle.
opposite rays - BA > and BC > are called opposite rays if B
is between A and C.
ordered pair - Unique point on the coordinate plane.
origin - Point of intersection of the axis on the coordinate plane.
orthocenter - Point of concurrence of the altitudes of a triangle.
parallel lines - Two lines that lie in the same plane and do not
intersect.
parallel planes - Two planes that do not intersect.
parallel rays or segments - Two segments or rays, or the lines
that contain them, that do not intersect.
parallelogram - Quadrilateral with both pairs of opposite sides
parallel.
perimeter (of a polygon) - Sum of the lengths of the sides.
perpendicular (lines) - Two lines that intersect to form right
angles.
perpendicular bisector of a segment - Line, ray, segment, or
plane that is perpendicular to a segment at its midpoint.
pi (π) - Ratio of the circumference to the diameter of a circle.
plane - A flat surface with no thickness that extends without end
in all directions.
plane angle (dihedral angle) - Angle formed by a plane that is
perpendicular to its edge.
point - Has no size and no dimension, merely position.
polygon - Figure consisting of three or more coplanar segments
intersecting only at end points with no two segments collinear.
polyhedron - Geometric figure made up of a finite number of
polygons that are joined by pairs along their sides and that
enclose a finite portion of space.
postulate (axiom) - Statement accepted as true without proof.
prism - Polyhedron with two congruent faces contained in parallel planes, and its other faces parallelograms.
proof - Logical sequence of statements with their supporting
reasons.
proportion - Equality of two ratios.
protractor - Instrument used to determine the measure of an
angle in degrees.
prove - Conclusion to be reached in a proof.
pyramid - Polyhedron with all faces except one having a
common vertex.
quadrant - One of four regions of the coordinate plane.
quadrilateral - A polygon with four sides.
radius (circle) - Segment extending from the center to any
point on the circle (plural: radii).
radius (regular polygon) - Segment that joins the center to a
vertex.
ratio - Given two numbers x and y, y not equal to 0, a ratio is
the quotient of x divided by y.
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ray - Set of points on a line that consists of a segment, AB, and
all points C such that B is between C and A.
rectangle - Parallelogram that has a right angle.
regular polygon - Polygon that is both equilateral and equiangular.
regular polyhedron - A polyhedron in which all the faces are
congruent regular polygons.
regular prism - Prism with regular polygons as bases.
regular pyramid - Pyramid with a regular polygonal base and
congruent lateral edges.
remote interior angle - An interior angle that is not adjacent to
the given exterior angle.
rhombus - Parallelogram with consecutive sides congruent.
right angle - Angle whose measure is 90.
right circular cone - Circular cone whose axis is perpendicular
to the base.
right cylinder - Cylinders whose axis perpendicular to the
bases.
right prism - Prism with lateral edges perpendicular to the
planes of the bases.
right triangle - Triangle with one right angle.
scale factor - Ratio between the corresponding sides of similar
polygons.
scale factor (similar solids) - Ratio of corresponding lengths.
scalene triangle - Triangle in which no sides are congruent.
secant - Line, ray, or a segment that contains a chord of a circle.
sector (circle) - Region bounded by two radii and their
intercepted arc.
segment - Set of points on a line that consist of two points
called the endpoints, and all points between them.
segment (circle) - Region bounded by an arc and the chord of
the arc.
semicircle - Arc whose endpoints are the endpoints of a diameter.
sides (polygon) - Segments that determine a polygon.
sides (angle) - Rays that form an angle.
similar - Polygons with corresponding angles congruent and
lengths of corresponding sides in proportion.
similar solids - Solids having similar bases and corresponding
lengths proportional.
sine - The sine of an acute angle of a right triangle is the ratio
of the leg opposite the angle to the length of the hypotenuse.
skew lines - Two lines that do not lie in the same plane and do
not intersect.
slant height (regular pyramid) - Distance from the vertex to
the base edge.
slant height (right circular cone) - Distance from the vertex to
any point of the circle that forms the base.
space - The set of all points.
sphere - Set of all points in space that are a given distance from
a given point called the center.
square - A quadrilateral with four right angles and four
congruent sides.
square unit - Square region having sides that measure one unit
in length.
supplementary angles - Two angles with measure whose sum
is 180. Each angle is called a supplement of the other.
tangent - The tangent of an angle in a right triangle is the ratio
of the length of the opposite leg to the length of the adjacent leg.
tangent circles - Two coplanar circles which are tangent to the
same line at the same point.
tangent segment - A segment that contains a point of tangency
and another point of a tangent line to a circle.
tangent to a circle - Line in the plane of the circle that intersects
the circle in exactly one point.
theorem - A statement which must be proved before being
accepted.
total area - Sum of the lateral area and the area of the base(s).
transversal - Line that intersects two or more coplanar lines at
different points.
trapezoid - Quadrilateral with exactly one pair of parallel sides.
triangle - Set of points that consists of the figure formed by
three segments connecting three non-collinear points.
vertex (angle) - Common endpoint of the rays that form an
angle.
vertex angle - Angle opposite the base of an isosceles triangle.
vertex (polygon) - Intersection point of two consecutive sides
of a polygon.
vertex (pyramid) - The common vertex.
vertical angles - Two non-adjacent angles formed by two
intersecting lines.
vertices (polyhedron) - Points where the edges intersect.
volume - Amount of space occupied by a figure.
©2000 The Teaching Company L. P. and TMW Media Group
GEOMETRY DEFINITIONS
acute angle - Angle whose measure is between zero and 90.
acute triangle - Triangle with three acute angles.
adjacent angles - Two coplanar angles that have a common
vertex, a common side, and have no common interior points.
adjacent non-overlapping arcs - Arcs with exactly one point
in common.
adjacent sides of a polygon - Sides which intersect at a vertex.
alternate exterior angles - Pair of non-adjacent angles, both
exterior, on opposite sides of the transversal.
alternate interior angles - Pair of non-adjacent angles, both
interior, on opposite sides of the transversal.
altitude (cone) - Perpendicular segment joining the vertex to
the plane of the base.
altitude (cylinder) - Perpendicular segment joining the bases.
altitude (parallelogram) - Segment perpendicular to the base
and joining the base to the opposite side.
altitude (prism) - Segment perpendicular to the planes of both
bases.
altitude (trapezoid) - Segment that is perpendicular to, and has
its endpoints on, the bases of the trapezoid.
altitude (triangle) - Segment that is perpendicular from a
vertex to the line containing the opposite side.
angle (triangle) - Union of two noncollinear rays with a
common endpoint.
angle bisector (in a triangle) - Segment that bisects an angle of
a triangle and has one endpoint on the opposite side.
angle of depression - Angle drawn down from the horizontal.
angle of elevation - Angle drawn up from the horizontal.
annulus - A region bounded by two concentric circles.
apothem (regular polygon) - Distance from the center to a
side.
arc length - Portion of the circumference of a circle.
area - Size of the region enclosed by the figure.
auxiliary figures - Lines, segments, rays, or points added to a
figure in order to facilitate a proof or an understanding of a
problem.
axis (cone) - Perpendicular segment joining the vertex to the
base.
axis (cylinder) - Segment joining the centers of the bases.
base (isosceles triangle) - The side opposite the vertex angle.
base angles (isosceles triangle) - Angles that include the base.
base angles (trapezoid) - Angles that include each base.
based edges (pyramid) - Edges of the base.
base (parallelogram) - One side of the parallelogram.
base (pyramid) - Face that does not contain the vertex.
bases (prism) - Two congruent, parallel faces.
bases (trapezoid) - The parallel sides.
between (points) - Given three collinear points, X, Y and Z, Y
is between X and Z if and only if XY + YZ = XZ.
between (rays) - Given three coplanar rays
or >, and
OA >,
OB >
, or > is between
OA > and
OB > if and only if
m AOT + m TOB = m AOB.
biconditional - “If and only if” statement formed by combining
a conditional and its converse into one statement.
bisector (angle) - Ray that separates an angle into two angles of
equal measures.
bisector (segment) - Any line, segment, ray, or plane that intersects a segment at its midpoint.
center (circle) - The given point from which every point on the
circle is equidistant.
center (regular polygon) - Center of the circumscribed circle.
central angle (circle) - Angle whose vertex is the center of the
circle and whose sides are radii.
central angle (regular polygon) - Angle with its vertex at the
center and its sides two consecutive radii.
centroid - Point of concurrence of the medians of a triangle.
chord - Segment joining two points on a circle.
circle - Set of all points in a plane that are a given distance from
a given point called the center.
circumcenter - Point of concurrence of the perpendicular bisectors of the sides of a triangle.
circumscribed around the polygon - Each vertex of the polygon
is a point on the circle.
circumference - Distance around a circle.
collinear - Points that lie on the same line.
common external tangent - Line tangent to two coplanar
circles that does not intersect the segment joining the centers of
the two circles.
common internal tangent - Line tangent to two coplanar
circles that intersects the segment joining the centers of the two
circles.
complementary angles - Two angles whose measures sum to
90.
concave polygon - Polygon in which any of the lines containing the sides also contain points in the polygons interior.
concentric circles - Coplanar circles of different radii with a
common center.
conclusion - “Then” part of a conditional statement.
concurrent lines - Lines that converge, or intersect, in one
common point.
conditional - Statement formed by joining two statements,
p and q, with the words if and then.
cone - Pyramid-like solid with a circular base.
congruent angles - Angles that have equal measures.
congruent arcs - Arcs in the same or congruent circles with
equal measures.
congruent circles - Circles having congruent radii.
congruent quadrilaterals - Quadrilaterals with corresponding
angles and corresponding sides congruent.
congruent segments - Segments having equal measures.
congruent triangles - Triangles whose corresponding angles
and corresponding sides are congruent.
construction - Creating a figure using only a straight edge and
a compass.
contrapositive - Statement related to a conditional statement in
the form: If ~ b, then ~ a.
converse - Statement related to a conditional statement in the
form: If b, then a.
convex polygon - Polygon in which the lines containing the
sides do not contain points in the polygon’s interior.
coordinate - Number paired with each point on a numbered line.
coordinate plane - Plane of the x-axis and the y-axis.
coplanar - Points that lie on the same plane.
corollary - Theorem whose justification follows from another
theorem.
corresponding angles - Pair of non-adjacent angles - one
interior, one exterior - both on the same side of the transversal.
cosine - In right triangle ABC with acute
A,
length of adjacent leg
cosine A =
length of hypotenuse
cylinder - Prism-like solid with circular bases.
decagon - A polygon with ten sides.
deductive reasoning - Reasoning logically from given
statements to a desired conclusion.
diagonal - Segment that joins two non-consecutive vertices.
diameter - Chord containing the center of a circle.
dihedral angle - Union of two noncoplanar half-planes that
have the same edge.
distance - Absolute value of the difference of the coordinates of
two distinct points on a line.
distance (from point to line) - Length of the perpendicular
from the point to the line.
dodecagon - A polygon with twelve sides.
edge (dihedral angle) - Intersection of the two noncoplanar
half-planes.
edge (plane) - Line that separates a plane into two half-planes.
edges (polyhedron) - Intersections of the sides.
equiangular - Has congruent angles.
equidistant - Equally distant from.
equilateral - With congruent sides.
exterior angle - An angle that is adjacent and supplementary to
one of the angles of a triangle.
externally tangent circles - All points of one circle are exterior
to those of the other, except the point where the circles are
tangent to the same line.
extremes - First and fourth terms of a proportion.
faces (dihedral angle) - The non-coplanar half-planes forming
the angle.
formal proof - A logical argument in which each statement
requires justification.
geometric mean - x is the geometric mean between positive
numbers p and q if and only if a/x = x/b, where x > 0.
given - Hypothesis of a proof.
great circle - Intersection of a sphere and a plane that contains
the center of the sphere.
half-planes - Two halves of a plane that are separated by a line.
height - (Cylinder, cone, prism, parallelogram, triangle,
trapezoid) Length of the altitude.
hypotenuse - Side of the right triangle that is opposite the right
angle.
hypothesis - “If” part of a conditional statement.
incenter - Point of concurrence of the angle bisectors of a
triangle.
inductive reasoning - Making a conclusion based upon several
past observations.
inscribed angle - Angle with its vertex on the circle and its
sides containing chords of the circle.
inscribed circle - A circle about which a polygon is circumscribed.
inscribed polygon - A polygon whose sides are chords of a
circle.
intercepted arc - The arc AB is called the intercepted arc of
inscribed angle ACB.
internally tangent circles - One circle in the interior of the
other, except for the point where the circles are tangent to the
same line.
intersection (two figures) - The set of points that lie in both
figures.
inverse - Statement related to conditional statement in the form:
If ~ a then ~ b.
isosceles triangle - Triangle in which at least two sides are
congruent.
kite - A quadrilateral in which exactly one diagonal is the
perpendicular bisector of the other.
lateral area - Sum of the areas of the lateral faces.
lateral edges (prism) - Intersections of the lateral faces.
lateral edges (pyramid) - Intersections of the lateral faces.
lateral faces (prism) - Parallelogram faces.
lateral faces (pyramid) - Faces that contain the vertex.
lateral surface (cone) - Set of all points not in the base.
legs (isosceles triangle) - Two congruent sides.
legs (right triangle) - Sides opposite the acute angles.
legs (trapezoid) - Non-parallel sides.
line - Infinitely many points extending in both directions.
linear pair - Two angles that are adjacent and whose noncommon sides are opposite rays.
locus - Set of points satisfying one or more given conditions.
major arc - Arc with measure > 180.
means - Second and third terms of a proportion.
measure (dihedral angle) - Measure of a plane angle of the
dihedral angle.
measure (major arc) - Difference between the measure of its
related minor arc and 360.
measure (minor arc) - Measure of its central angle.
measure (length) (segment) - Distance between the endpoints
of the segment.
measure (semicircle) - 180.
median (trapezoid) - Segment that joins the midpoints of the
legs.
median (triangle) - Segment that extends from a vertex to the
midpoint of the opposite side.
midpoint (segment) - Point that divides a segment into two
congruent segments.
minor arc - Less than a semicircle.
negation (statement) - Formed by using the word not.
noncollinear - Points that are not collinear.