Essential Geometry Terms and Definitions Glossary
A
Acute Angle
An angle measuring less than 90°.
Acute Triangle
A triangle where all three interior angles are acute (less than 90°).
Altitude of a Triangle
A perpendicular segment from a vertex to the opposite side or to a line containing the opposite side.
Angle
It is formed by two rays that share a common endpoint, provided that the two rays are noncollinear.
Angle Bisector
A ray that contains the vertex and divides the angle into two congruent angles.
Arc
Two points on the circle and a continuous part of the circle between the two points. Arcs are classified into three types:
- Semicircle: An arc whose endpoints are the endpoints of the diameter.
- Minor Arc: An arc that is smaller than a semicircle.
- Major Arc: An arc that is larger than a semicircle.
Area
A function that assigns a non-negative real number to each two-dimensional geometric shape.
B
Base
The side opposite the vertex angle (often used in the context of triangles or 3D figures).
Base Angles
The two angles opposite the two sides of equal length (typically in an isosceles triangle).
C
Central Angle
An angle whose vertex is the center of a circle and whose sides are two different radii.
Circle
A set of points at a given distance (radius) from a given point (center).
Circumference
The distance around the circle.
Chord
A line segment whose endpoints lie on a circle.
Collinear
Points that lie on the same line.
Common Endpoint (Vertex)
The vertex, which is the common endpoint shared by the two rays forming the sides of an angle.
Complementary Angles
A pair of angles whose measures sum to 90°.
Concave Polygon
A polygon where at least one diagonal lies partially or entirely outside the polygon.
Concentric Circles
Two or more circles that share the same center.
Cone
A three-dimensional figure that has a circular base. The vertex is the point of greatest perpendicular distance from the base.
Congruent
Figures or objects are congruent if and only if they have the same size and shape (equal measure). When two segments have equal measures or lengths, they are congruent. Congruent segments are shown by making identical marks on figures.
Convex Polygon
A polygon where all diagonals lie entirely inside the polygon.
Coplanar
Points or lines that lie in the same plane.
D
Diagonal of a Polygon
A line segment that connects two nonconsecutive vertices of a polygon (applies to both convex and concave polygons).
Diameter
A special chord that passes through the center of a circle.
E
Edge
A segment where two faces of a polyhedron intersect.
Equiangular Polygons
Polygons in which all interior angles are equal.
Equilateral Triangle
A triangle in which all sides are congruent.
Equilateral Polygons
Polygons in which all sides are equal in length.
F
Faces
The flat polygonal surfaces of a polyhedron.
Flowchart
A visual way to organize all steps in a complicated procedure in a proper order.
G
Geometry
A part of mathematics that studies and analyzes locations, spatial views, geometric figures, and geometric objects.
Given Information
The initial part of a proof that is assumed to be true.
H
Hemisphere
A half sphere and its circular base.
I
Inscribed Angle
An angle whose vertex is a point on a circle and whose sides are two chords.
Isosceles Triangle
A triangle with two congruent sides.
Intercepted Arc
Corresponding to an angle, this is the portion of the circle that lies in the interior of the angle, together with the endpoints of the arc.
L
Line
A one-dimensional figure that has infinite length and extends forever in both directions.
Line of Reflection
The given line across which a figure is reflected during a transformation.
Line Segment
Consists of two points, called the endpoints of the segment, and all the points between them that are collinear with the two endpoints.
Linear Pair of Angles
Two adjacent angles that share a vertex and a common side, and whose non-common sides form a straight line.
M
Measure of an Angle
The smallest amount of rotation about the vertex from one ray to the other, measured in degrees.
Median
The segment connecting the vertex of a triangle to the midpoint of its opposite side.
Midpoint of a Segment
The point on the segment that is the same distance from both endpoints. The midpoint bisects the segment.
Monohedral Tessellation
A tessellation where all shapes used are congruent.
N
Nonrigid Transformation
A transformation where the resulting figure is not congruent to the original figure (it changes size or shape).
O
Oblique Prism
A prism that is not a right prism (its lateral faces are not perpendicular to the bases).
Obtuse Angle
An angle measuring more than 90° and less than 180°.
Obtuse Triangle
A triangle containing one angle that measures more than 90°.
P
Parallel Lines
Lines in the same plane (coplanar) that never intersect.
Parallelogram
A quadrilateral with two pairs of parallel sides.
Perimeter
The sum of the lengths of the sides of a polygon.
Perpendicular Bisector of a Chord Conjecture
The intersection point of the perpendicular bisectors of two non-parallel chords of a circle is the center of the circle.
Perpendicular Lines
Lines that intersect to form a 90° (right) angle.
Plane
A two-dimensional surface that has length and width but no thickness.
Point
A precise location or place on a plane, usually represented by a dot.
Polygons
A closed figure in a plane, formed by connecting line segments endpoint to endpoint, with each segment intersecting exactly two others.
Polyhedron
A solid formed by polygons (faces) that enclose a single region of space.
Prism
A solid figure with two congruent, parallel polygonal faces (called bases). The remaining faces are called lateral faces.
Proof
A sequence of statements, starting with a given set of premises and leading to a valid conclusion.
Proportion
A statement of equality between two ratios. For example: 6/18 = 2/9.
Protractor
The geometry tool used to measure angles.
Pyramids
Polyhedrons with only one polygonal base and a common vertex (apex) to all triangular lateral faces.
Q
Quadrilaterals
A geometric figure that has four sides and four angles.
R
Ratio
An expression that compares two quantities by division. The ratio of quantity “a” to quantity “b” can be written in these three forms:
- a/b
- a to b
- a:b
Ray
When a line begins at a point (endpoint) and extends infinitely in one direction. It is named with two letters: the first is the endpoint, and the second is any other point that the ray passes through.
Rectangle
An equiangular parallelogram.
Reflection
A transformation in which every point of a figure appears an equal distance on the opposite side of a given line (the line of reflection).
Reflex Angle
An angle measure greater than 180° and less than 360°.
Regular Polygons
Polygons that are both equilateral (equal sides) and equiangular (equal angles).
Regular Polyhedron
A polyhedron where all faces are congruent regular polygons and the faces meet at each vertex in exactly the same way.
Regular Tessellation
A tessellation composed entirely of congruent regular polygons.
Rhombus
An equilateral parallelogram.
Right Angle
An angle measuring exactly 90°.
Right Triangle
A triangle that contains one angle measuring 90°.
Rigid Transformation (Isometry)
A transformation where the resulting figure is congruent to the original figure (it preserves size and shape).
Rotation
A transformation in which all points in the original figure rotate an identical number of degrees about a fixed center point.
S
Scalene Triangle
A triangle with no congruent sides; all sides have different lengths.
Show Information (Conclusion)
The conclusion or statement that must be logically demonstrated in a proof.
Semiregular Tessellation
A tessellation using two or more types of regular polygons such that every vertex arrangement is identical.
Solid
A geometric figure that has three dimensions (length, width, and height).
Spatial Relation
Describes the location of an object in relation to some other object.
Sphere
The set of all points in space equidistant from a given point (the center).
Supplementary Angles
A pair of angles whose measures sum to 180°.
Square
A regular quadrilateral; a figure with four equal sides and four right angles (90°).
T
Tangent
A line that intersects a circle at exactly one point.
Tessellations (Tiling)
A repeating pattern of shapes that covers a plane without any gaps or overlaps.
Tetrahedron
A polyhedron with four faces. (The prefix system for polyhedrons generally follows that of polygons.)
Translation
A transformation in which all points of a figure move the same distance along parallel paths to form an image.
Transformation
The process of moving all the points of a geometric figure according to certain rules to create an image of the original figure.
Trapezoid
A quadrilateral that has at least one pair of parallel sides.
Triangle
A polygon with three vertices and three sides (line segments).
V
Vertex (Polyhedron)
The point of intersection of three or more edges.
Vertex Angle (Isosceles Triangle)
In an isosceles triangle, the angle formed by the two sides of equal length.
Vertical Angles
Angles formed by two intersecting lines; they share a common vertex but not a common side, and they are congruent.