point
a location
circumference
the distance around a circle
coplanar
points that lie oin the same plane
perimeter
the sum of the lengths of the sides of a polygon
circumference
the distance around a circle
undefined terms
points, planes, lines in geometry
acute angle
An angle with a measure greater than 0° and less than 90°
adjacent angles
Angles that have the same vertex, share a common side, and do not overlap
angle
A figure formed by two rays with a common endpoint
angle bisector
A ray whose endpoint is the vertex of the angle and is located in the interior of the angle. It separates a given angle into two angles with equal measure.
area
The number of square units needed to cover a surface enclosed by a geometric figure
base
The faces on the top and bottom of the figure
between
Point R is between points P and Q if and only if R, P, and Q are collinear and PR + RQ = PQ
collinear
Three or more points that lie on the same line
complementary angles
Two angles are complementary if the sum of their measures is 90°
concave
A polygon for which a point on at least one of its diagonals lies outside the polygon
cone
A three-dimensional figure with one circular base and one vertex. A curved surface connects the base and the vertex
congruent
Having the same measure
construction
The process of drawing a figure using only a compass and a straightedge
convex
A polygon for which all diagonals are located in the interior of the polygon
cylinder
A solid figure whose bases are formed by congruent circles in parallel planes and whose lateral surface is curved. The segment whose endpoints are the centers of the circular bases is called the axis of the cylinder. The altitude is a segment perpendicular to the bases with an endpoint in each base.
degree
The most common unit of measure for angles
distance
The distance between two points
edge
The intersection of faces of a three-dimensional figure
equilateral polygon
A triangle having all three sides congruent and all three angles congruent
equiangular polygon
A triangle with three congruent angles
exterior
All points outside the sides of the angle
face
surface of a figure
interior
All points between the two sides of an angle
intersection
The set of elements common to two or more sets as in compound inequalities and Venn diagrams
line
A never-ending straight path
linear pair
points upon a line
line segment
Part of a line containing two endpoints and all the points between them
midpoint
On a line segment, the point that is halfway between the endpoints
n-gon
A polygon with n sides
obtuse angle
An angle that measures more than 90° but less than 180°
opposite rays
Two rays that are part of the same line and have only their endpoints in common. In the figure, and are opposite rays
perpendicular
Lines which meet to form right angles and whose slopes have a product of -1
plane
A two-dimensional flat surface that extends in all directions
point
A specific location in space with no size or shape
polygon
A simple closed figure in a plane formed by three or more line segments
polyhedron
A solid with four or more flat surfaces that are polygonal regions
prism
A polyhedron with two parallel, congruent faces called bases. A solid with the following characteristics: 1. Two faces, called the bases, are formed by congruent polygons that lie in parallel planes. 2. The faces that are not bases, called lateral faces, are formed by parallelograms. 3. The intersection of two adjacent lateral faces are called lateral edges and are parallel segments.
pyramid
A solid figure that has a polygon for a base and triangles for sides. A pyramid is named for the shape of its base. A solid with the following characteristics: 1. All the faces, except one, intersect at a common point called the vertex. 2. The face that does not intersect at the vertex is called the base. The base is formed by a polygon. 3. The faces meeting at the vertex are called lateral faces. They are formed by triangles.
ray
A part of a line that extends indefinitely in one direction from a fixed point
regular polygon
A polygon that has all sides congruent and all angles congruent
regular polyhedron
A polyhedron in which the faces are regular congruent polygons
right angle
An angle that measures exactly 90°
segment bisector
To separate something into two congruent parts
side
The segments that form a closed figure
space
A boundless three-dimensional set of all points
sphere
The set of all points in space that are a given distance from a given point, called the center. It has the following characteristics: 1. A radius is a segment whose endpoints are the center and a point on the sphere. 2. A chord is a segment whose endpoints are points on the sphere. 3. A diameter is a chord of the sphere that contains the center.
supplementary angles
Two angles are supplementary if the sum of their measures is 180°
surface area
The sum of the areas of all the faces of a three-dimensional figure
vertex
The common endpoint of the rays forming the angle
vertical angles
Opposite angles formed by the intersection of two lines
volume
The number of cubic units needed to fill the space occupied by a solid
algebraic proof
An expression consisting of one or more numbers and variables along with one or more arithmetic operations
conjecture
A conclusion reached that is based on inductive reasoning
conjunction
A compound statement formed by joining two statements with the word and
converse
The statement formed by exchanging the hypothesis and conclusion of a conditional statement
inverse
The statement formed by negating both the hypothesis and conclusion of a conditional statement
postulate
A rule of geometry that is accepted as being true without proof
theorem
A statement that can be justified by logical reasoning and must be proven before it is accepted as true
parallel lines
Lines in the same plane that never intersect and have the same slope
point-slope form
An equation of the form y - y1 = m(x - x1), where m is the slope and (x1, y1) is a given point on a nonvertical line
rate of change
The change in a quantity over time
skew lines
Two nonparallel lines that do not intersect. In the figure, and are skew segments
slope
The ratio of the change in the y-coordinates (rise) to the corresponding change in the x-coordinates (run) as you move from one point to another along a line
slope-intercept form
An equation of the form y = mx + b, where m is the slope and b is the y-intercept
transversal
A line that intersects two or more other lines to form eight or more angles
acute triangle
A triangle in which each angle measures less than 90°
base angles
The equal angles formed by the base and the congruent sides of an isosceles triangle
congruent polygons
Polygons that have the same shape and size
corresponding parts
Parts of congruent or similar figures that match
equiangular triangle
A triangle with three congruent angles
included angle
An angle formed by two given sides of a triangle
included side
A side common to two given angles of a triangle
isosceles triangle
A triangle with at least two congruent sides
reflection
A transformation in which a figure is flipped over a line of symmetry
right triangle
A triangle having one right angle
rotation
A transformation in which a figure is turned around a fixed point
scalene triangle
A triangle with no congruent sides
translation
A transformation in which a figure is slid in any direction
altitude
A line segment perpendicular to the base of a figure with endpoints on the base and on the vertex opposite the base
centroid
The point of intersection of the three medians of a triangle
circumcenter
The point of concurrency of the perpendicular bisectors of a triangle
concurrent lines
Three or more lines or segments that meet at a common point
incenter
The point of concurrency of the angle bisectors of a triangle
median
The middle number in a set of data when the data are arranged in numerical order. If the data has an even number, the median is the mean of the two middle numbers
orthocenter
The point of concurrency of the altitudes of a triangle
perpendicular bisector
A segment that is perpendicular to another segment and passes through that segment's midpoint
diagonal
A segment joining two nonconsecutive vertices of a polygon. In the figure, is a diagonal
isosceles trapezoid
A trapezoid with two congruent legs
kite
A quadrilateral with exactly two distinct pairs of adjacent congruent sides
legs
The sides of a right triangle that form the right angle
midsegment of a trapezoid
A segment with endpoints that are the midpoints of two sides of a triangle
parallelogram
A quadrilateral with both pairs of opposite sides parallel and congruent
rectangle
A parallelogram with four right angles
rhombus
A parallelogram with four congruent sides
square
A parallelogram with four congruent sides and four right angles
trapezoid
A quadrilateral with exactly one pair of parallel opposite sides