Two angles in a plane that have a common vertex and a common side but no common interior points.
Adjacent Arcs
Arcs of a circle that have exactly on point in common.
Alternate Interior Angles
Two nonadjacent interior angles on opposite sides of a transversal.
Altitude of a Parallelogram
Any segment perpendicular to the line containing a base from any point on the opposite side.
Altitude of a Trapezoid
Any segment perpendicular to a line containing one base from a point on the opposite base.
Altitude of a Triangle
The perpendicular segment from a vertex to the line containing the opposite side.
Angle
A figure formed by two rays that have the same endpoint. The two rays are called the sides of the angle. Their common endpoint is the vertex.
Apothem
The perpendicular distance from the center of a regular polygon to a side.
Auxiliary Line
A line, ray, or segment added to a diagram to help in a proof.
Axes
Usually, two perpendicular lines used to establish a coordinate system.
Axiom
A statement that is accepted without proof.
Base of a Parallelogram
Any side of a parallelogram can be considered its base. The term base may refer to the line segment or its length.
Biconditional
A statement that contains the words "if and only if."
Bisector of an Angle
The ray that divides the angle into two congruent adjacent angles.
Bisector of a Segment
A line, segment, ray, or plane that intersects the segment at its midpoint.
Center of a Regular Polygon
The center of the circumscribed circle.
Central Angle of a Circle
An angle with its vertex at the center of the circle.
Central Angle of a Regular Polygon
An angle formed by two radii drawn to consecutive vertices.
Chord
A segment whose endpoints lie on a circle.
Circle
The set of points in a plane that area given distance from a given point in the plane. The given point is the center, and the given distance is the radius.
Circumference of a Circle
The perimeter of a circle given by the limiting number approached by the perimeters of a sequence of regular inscribed polygons. For radius R, C=2xpiexr
Complementary Angles
Two angles whose measures have the sum 90.
Concentric Circles
Circles that lie in the same plane and have the same center.
Concentric Spheres
Spheres that the same center.
Conclusion
See if-then statement.
Concurrent Lines
Two or more lines that intersect in one point.
Conditional Statement
See if-then statement.
Cone
Both have circular bases and a vertex V. In the right cone, h is the length of the altitude, l is the slant height, and r is the radius.
Congruent Angles
Angles that have equal measures.
Congruent Arcs
Arcs, in the same circle or in congruent circles, that have equal measures.
Congruent Circles (or Spheres)
Circles (or Spheres) that have congruent radii.
Congruent Figures
Figures having the same size and shape.
Congruent Polygons
Polygons whose vertices can be matched up so that the corresponding parts (angles and sides) of the polygons are congruent.
Contraction
See dilation.
Contrapositive of a Conditional
The contrapositive of the statement If p, then q is the statement If not q, the not p.
Converse
The converse of the statement If p, then q is the statement If q, then p.
Convex Polygon
A polygon such that no line containing a side of the polygon contains a point in the interior of the polygon.
Coordinate Plane
The plane of the x-axis and the y-axis.
Coplanar Points
Points all in one plane.
Corollary of a Theorem
A statement that can be proved easily by applying the theorem.
Corresponding Angles
Two angles in corresponding positions relative to two lines.
Cosine (cos)
Cosine of Angle: cos A= Adjacent\Hypotenuse.
Counterexample
An example used to prove that an if-then statement is false. For that counterexample, the hypothesis is true and the conclusion is false.
Cube
A rectangular solid with square faces.
Cylinder
In a right cylinder, the segment joining the centers of the circular bases is an altitude. The length of an altitude is the height, h, of the cylinder. A radius of a base is a radius, r, of the cylinder.
Decagon
A 10-sided polygon.
Deductive Reasoning
Proving statements by reasoning from accepted postulates, definitions, theorems, and given information.
Diagonal
A segment joining two non-consecutive vertices of a polygon.
Diameter
A chord that contains the center of a circle.
Distance from a point to a line (or plane)
The length of the perpendicular segment from the point to the line (or plane).
Equiangular Triangle
A triangle with all angles congruent.
Equilateral Triangle
A triangle with all sides congruent.
Expansion
See Dilation.
Exterior Angle of a Triangle
The angle formed when one side of the triangle is extended.
Geometric Mean
If a, b, and x are positive numbers with a\x=x\b, then x is the geometric mean between a and b.
Golden Ratio
See Golden Rectangle.
Golden Rectangle
A rectangle such that its length l and width w satisfy the equation l\w=l+w\l. The ratio l:w is called the Golden Ratio.
Great Circle
The intersection of a sphere with any plane passing through the center of the sphere.
Height
The length of an altitude of a polygon or solid.
Heron's Formula
A formula for finding the area of a triangle when the lengths of its sides are known.
Hexagon
A 6-sided polygon.
Hypotenuse
In a right triangle the side opposite the right angle. The other two sides are called legs.
Hypothesis
See if-then statement.
If-Then Statement
A statement whose basic form is If p, then q. Statement p is the hypothesis and statement q is the conclusion.
Indirect Proof
A proof in which you assume temporarily that the conclusion is not true, and then deduce a contradcition.
Inductive Reasoning
A kind of reasoning in which the conclusion is based on several past observations.
Inscribed Angle
An angle whose vertex is on a circle and whose sides contain chords of the circle.
Inscribed Circle
See circumscribed circle.
Inscribed Polygon
See circumscribed polygon.
Intersection of Two Figures
The set of points that are in both figures.
Inverse of a Conditional
The inverse of the statement If p, then q, is the statement If not p, then not q.
Isometry
A transformation that maps every segment to a congruent segment. Also called a congruence mapping.
Isosceles Trapezoid
A trapezoid with congruent legs.
Isosceles Triangle
A triangle with at least two sides congruent.
Kite
A quadrilateral that has two pairs of congruent sides, but opposite sides are not congruent.
Lateral Area of a Prism
The sum of the areas of its lateral faces.
Lateral Edges of a Prism
See prism.
Lateral Edges of a Pyramid
See pyramid.
Lateral Faces of a Prism
See prism.
Lateral Faces of a Pyramid
See pyramid.
Legs of an Isosceles Triangle
The two congruent sides. The third side is the base.
Legs of a Right Triangle
See hypotenuse.
Legs of a Trapezoid
See trapezoid.
Length of a Segment
The distance between its endpoints.
Linear Equation
An equation whose graph is a line.
Major Arc
See minor and major arcs.
Measure of a Major Arc
See minor and major arcs.
Measure of a Minor Arc
See minor and major arcs.
Measure of an Angle
A unique positive number, less than or equal to 180, that is paired with the angle.
Measure of a Semicircle
See semicircles.
Median of a Trapezoid
The segment that joins the midpoints of the legs.
Median of a Triangle
A segment from a vertex to the midpoint of the opposite side.
Midpoint of a Segment
The point that divides the segment into two congruent segments.
Minor and Major Arcs
YZ is a minor arc of circle O. YXZ is a major arc. The measure of a minor arc is the measure of its central angle, here angleYOZ. The measure of a major arc is found by subtracting the measure of the minor arc from 360.
N-Gon
A polygon of n sides.
Oblique Solid
See cone, cylinder, prism.
Obtuse Solid
An angle with measure between 90 and 180.
Obtuse Triangle
A triangle with one obtuse angle.
Octagon
An 8-sided polygon.
Opposite Rays
Given three collinear points R, S, T: If S is between R and T, then ray SR and ray ST are opposite rays.
Parallel Line and Plane
A line and a plane that do not intersect.
Parallel Lines
Coplanar lines that do not intersect.
Parallelogram
A quadrilateral with both pairs of opposite sides parallel.
Parallel Planes
Planes that do not intersect.
Pentagon
A 5-sided polygon.
Perimeter of a Polygon
The sum of the lengths of its sides.
Perpendicular Bisector of a Segment
A line that is perpendicular to the segment at its midpoint.
Perpendicular Line and Plane
A line and a plane are perpendicular if and only if they intersect and the line is perpendicular to all lines in the plane that pass through the point of intersection.
Perpendicular Lines
Two lines that intersect to form right angles.
Point of Tangency
See tangent to a circle.
Polygon
A plane figure formed by coplanar segments such that 1. each segment intersects exactly two other segments, one at each endpoint; and 2. no two segments with a common endpoint are collinear.
Postulate
A statement that is accepted without proof.
Prism
The solids shown are Prisms. The shaded faces are the bases (congruent polygons lying in parallel planes). The other faces are lateral faces and all are parallelograms. Adjacent lateral faces intersect in parallel segments called lateral edges. An altitude of a prism is a segment joining the two base planes and perpendicular to both. The length of an altitude is the height, h, of the prism.
Proportion
An equation stating that two ratios are equal. The first and last terms are the extremes; the middle terms are the means.
Pyramid
Point V is its vertex; the pentagon ABCDE is its base. The five triangular faces meeting at V are lateral faces; they intersect in segments called lateral edges. The segment from the vertex perpendicular to the base is the altitude, and its length is the height, h, of the pyramid. In a regular pyramid, the base is a regular polygon, all lateral edges are congruent, all lateral faces are congruent isosceles triangles, and the altitude meets the base at its center. The height of a lateral face is the slant height of the pyramid.
Pythagorean Triple
Any triple of positive integers a, b, and c, such that a squared + b squared= c squared.
Quadrant
Any one of the four regions into which the plane is divided by the coordinate axes.
Quadrilateral
A 4-sided polygon.
Radius of a Circle
See circle.
Radius of a Regular Polygon
The distance from the center to a vertex.
Radius of a Right Cylinder
See cylinder.
Ratio
The ratio of x to y (y is not equal to 0) is x\y and is sometimes written x:y.
Ray
The ray AC consists of segment AC and all other points P such that C is between A and P. The point named first, here A, is the endpoint of Ray AC.
Rectangle
A quadrilateral with four right angles.
Rectangular Solid
A right rectangular prism.
Regular Polygon
A polygon that is both equiangular and equilateral.
Regular Pyramid
See pyramid.
Remote Interior Angles
See exterior angle of a triangle.
Rhombus
A quadrilateral with four congruent sides.
Right Angle
An angle with measure 90.
Right Solid
See one, cylinder, prism.
Right Triangle
A triangle with one right angle.
Same-Side Interior Angles
Two interior angles on the same side of a transversal.
Scale Factor
For similar polygons, the ratio of the lengths of two corresponding sides.
Scalene Triangle
A triangle with no sides congruent.
Secant of a Circle
A line that contains a chord.
Sector of a Circle
A region bounded by two radii and an arc of the circle.
Segment of a Line
Two points on the line and all points between them. The two points are called the endpoints of the segment.
Semicircles
The two arcs of a circle that are cut off by a diameter. The measure of a semicircle is 180.
Sides of an Angle
See angle.
Sides of a Triangle
See triangle.
Similar Polygons
Two polygons are similar if their vertices can be paired so that corresponding angles are congruent and corresponding sides are in proportion.
Similar Solids
Solids that have the same shape but not necessarily the same size.
Sine(Sin)
Sine of Angle A= BC\AB Sin of Angle A = opposite\hypotenuse.
Skew Lines
Lines that are not coplanar.
Slant Height of a Regular Pyramid
See pyramid.
Slant Height of a Right Cone
See cone.
Space
The set of all points.
Sphere
The set of all points in space that are a given distance from a given point.
Square
A quadrilateral with four right angles and four congruent sides.
Straight Edge
An angle with measure of 180.
Supplementary Angles
Two angles whose measures have the sum 180.
Tangent(tan)
Tangent of Angle A = BC\AC Tan of Angle A = opposite\adjacent.
Tangent Circles
Coplanar circles that are tangent to the same line at the same point.
Tangent to a Circle
A line in the plane of the circle that intersects the circle in exactly one point, called the point of tangency.
Theorem
A statement that can be proved.
Total Area of a Prism
The sum of the areas of all its faces.
Transversal
A line that intersects two or more coplanar lines in different points.
Trapezoid
A quadrilateral with exactly one pair of parallel sides, called bases. The other sides are legs.
Triangle
The figure formed by three segments joining three noncollinear points. Each of the three points is a vertex of the triangle and the segments are the sides.
Venn Diagram
A circle diagram that may be used to represent a conditional.
Vertex Angle of an Isosceles Triangle
The angle opposite of the base.
Vertex of an Angle
See angle.
Vertex of a Pyramid
See pyramid.
Vertex of a Triangle
See triangle.
Vertical Angles
Two angles whose sides form two pairs of opposite rays.
