Acute Angle
An angle whose measure is more than zero degrees and less than 90 degrees.
Adjacent Angles
Two angles that share common side and a vertex but do not share any interior points.
Altitude
A perpendicular line from a vertex to the opposite side or to a line containing the opposite side - a triangle altitude can be inside, outside or one of the adjacent sides of the 90 degree angle.
Angle
Two rays that intersect at their endpoints only. The measure of an angle is less than or equal to 180 degrees.
Angle Bisector
A ray or line that passes through the vertex of an angle and forms two congruent angles that are half the measure of the original angle.
Area
The amount of two dimensional space within the borders of a plane figure. It is measured in square units.
Area of a Circle
The two-dimensional space within the boundary of a circle. A = (r^2)(pi) where r = radius.
Bisect
To split into two congruent parts.
Bisector
A line that cuts another line or angle exactly in half.
Circumference of a Circle
The distance around a circle. C = d(pi), where d = diameter. OR C = 2r(pi), where r = radius
Circle
In 2-dimensional space the set of all points that are a given distance from a given point
Collinear
Three or more points that lie in the same straight line.
Compass
An instrument used to draw circles and to mark off equal lengths (arc marks)
Complementary Angles
Two angles whose measures add up to 90 degrees. These two angles do not have to share any points.
Congruent
Geometric shapes that are the same shape and have the same measure are congruent.
Conjecture
A generalization made as a result of inductive reasoning.
Consecutive Vertices
Two vertices of a polygon that are endpoints of the same side.
Coplanar
Three or more non-collinear points, or a line and non-collinear points, or two or more lines, that are on the same plane are coplanar.
Equilateral Triangle
A triangle with all three sides congruent. (A regular triangle.)
Figure
A set of points in a plane.
Geometric constructions
A set of instructions for drawing points, lines, and circles, and figures in the plane.
Great Circle
The intersection of a sphere and a plane containing the center of the sphere. A great circle divides a sphere into two hemispheres. A line in spherical geometry.
Hemisphere
Half of a sphere with a circular base.
Hypotenuse
The longest side of a right triangle. It is opposite the right angle.
Length of a Segment
The distance between two points.
Line
Undefined term in Euclidean Geometry. A straight path that extends in two opposite directions through space. A line has no width or depth is infinite in length and made up of an infinite number of points (one dimension). Name a line with two points or one
Line Segment
A portion of a line that has definite length, and two endpoints. Name the line segment by its two endpoints in any order.
Linear Pair of Angles
Two adjacent angles whose unshared sides form a straight angle (or line.) A property of Linear Pairs is that the angles are supplementary. (Linear Pair Postulate)
Measure of a line segment
The length of a line segment, usually given in mm, cm, in, ft, or some other linear unit of measure. Always positive.
Measure of an angle
The amount of turning about the vertex from one side to the other. The measure of an angle is given in degrees or radians.
Midpoint
The point of a segment that splits the segment into two congruent segments. If point B is between A and C and the midpoint of AC then, AB = BC.
Midpoint formula (x, y grid)
X1 + X2 divided by 2, Y1 + Y2 divided by 2 are the (x, y) coordinates for the midpoint
Non-Collinear
Three or more points that do not lie on the same straight line.
Non-Coplanar
Four or more points that do not lie in the same plane.
Obtuse Angle
An angle whose measure is more than 90 degrees and less than 180 degrees.
Parallel Lines
Two or more coplanar lines that do not intersect. They have the same slope.
Perimeter
The sum of the lengths of the sides of a polygon.
perpendicular
Lines that intersect and form a 90 degree angle
Perpendicular bisector
A line that creates a 90 degree angle and cuts another line segment exactly in half
Perpendicular Lines
Two or more coplanar lines that intersect to form right angles. Their slopes are negative reciprocals of each other and their product equals -1.
Plane
Undefined term in Euclidean Geometry. a two dimensional (perfectly flat surface) that extends forever (infinite length and width) without end and has no thickness or depth. Name a plane with a capital letter or three non-collinear points.
Point
Undefined term in Euclidean Geometry. A location in space. No measure (length, width or depth). Zero dimension. Name a point with one upper case letter.
Postulate
A statement accepted without proof.
Proof
A logical argument in which each statement you make is backed up by a statement that is accepted as true.
Pythagorean Theorem
In a right triangle, where a and b are legs, and c is the hypotenuse, a^2 + b^2 = c^2.
Ray
A portion of a line that has only one endpoint and infinite length. Name the ray with the endpoint first and another point second that shows the direction the ray extends.
Right Angle
An angle whose measure is exactly 90 degrees.
Right Triangle
A triangle with one right angle and two acute angles. The two acute angles are complementary.
Segment
Part of a line that has two end points.
Segment Bisector
A line, ray, segment, or plane that passes through only the midpoint of a line segment. It creates two congruent segments that are half as long as the original segment.
Side of an Angle
One of the rays that form an angle.
Skew Lines
Two or more non-coplanar lines that do not intersect.
Sphere
In 3-dimensional space the set of all points that are a given distance from a given point.
Straight Angle
An angle whose measure is exactly 180 degrees.
Straightedge
An object that can be used to draw straight lines.
Supplementary Angles
Two angles whose measures add up to 180 degrees. These two angles do not have to share any points.
The Undefined Terms of Geometry
points, lines and planes
Triangle
A polygon with three sides.
Vertex of an Angle
The common endpoint of the two rays that form the angle.
Vertical Angles
The two non adjacent angles formed by intersecting lines that share only a vertex.
Distance
The amount of space between two objects.
Distance Formula
d = �[( x? - x?)? + (y? - y?)?]