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Geometry Terms
Terms and descriptions
135
Mathematics
Not Applicable
01/24/2009
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Term
acute angle
 Definition
An angle whose measure is greater than 0 and less than 90 (degrees).
Term
acute triangle
 Definition
A triangle in which all three angles are acute.
Term
alternate exterior angles
 Definition
A pair of angles in the exterior of a figure formed by two lines and a transversal, lying on alternate sides of the transversal and having different vertices.
Term
alternate interior angles
 Definition
A pair of angles in the interior of a figure formed by two lines and a transversal, lying on alternate sides of the transversal and having different vertices.
Term
altitude (of triangle)
 Definition
A perpendicular segment from the vertex of a triangle to the opposite side, extended if necessary.
Term
angle
 Definition
A figure formed by two rays with a common endpoint.
Term
angle of depression
 Definition
The angle between a downward line of sight and the horizontal.
Term
angle of elevation
 Definition
The angle between an upward line of sight and the horizontal.
Term
annulus
 Definition
A region bounded by two concentric circles.
Term
apothem
 Definition
A segment joining the center of a regular polygon to the midpoint of one of the polygon's sides.
Term
arc
 Definition
A figure consisting of two points on a circle and all points on the circle needed to connect them by a single path.
Term
area
 Definition
The number of square units of space within the boundary of a closed region.
Term
arithmetic mean
 Definition
The average of two numbers. The arithmetic mean of the numbers a and b, for example, is (a+b)/2.
Term
auxiliary line
 Definition
A line introduced into a diagram for the purpose of clarifying a proof.
Term
base (of an isosceles triangle)
 Definition
In a nonequilateral isosceles triangle, the side that is congruent to neither of the other sides.
Term
base (of trapezoid)
 Definition
Either of the two parallel sides of a trapezoid.
Term
base angle
 Definition
In an isosceles triangle or trapezoid, the angle formed by a base and an adjacent side.
Term
bisect
 Definition
To divide a segment or an angle into two congruent parts.
Term
center (of arc)
 Definition
The center of the circle of which an arc is a part.
Term
central angle
 Definition
An angle whose vertex is at the center of a circle.
Term
centroid
 Definition
The point of concurrency of the medians of a triangle.
Term
chord
 Definition
A segment joining two points on a circle.
Term
chord-chord angle
 Definition
An angle formed by two chords that intersect at a point inside a circle but not at the circle's center.
Term
circle
 Definition
The set of all points in a plane that are a given distance from a given point in the plane. (That point is called the circle's center.)
Term
circumcenter
 Definition
A point associated with a polygon, corresponding to the center of the polygon's circumscribed circle. (The circumcenter of a triangle is the point of concurrency of the perpendicular bisectors of the triangle's sides.)
Term
circumference
 Definition
The perimeter of a circle.
Term
circumscribed polygon
 Definition
A polygon each of whose sides is tangent to a circle.
Term
collinear
 Definition
Lying on the same line.
Term
common tangent
 Definition
A line tangent to two circles (not necessarily at the same point)--called a common internal tangent if it lies between the circles or a common external tangent if it does not.
Term
complementary angles
 Definition
Two angles whose sum is 90 degrees (a right angle).
Term
compound locus
 Definition
The intersection of two or more loci.
Term
concentric circles
 Definition
Two or more coplanar circles with the same center
Term
conclusion
 Definition
The "then" clause in a conditional statement.
Term
concurrent lines
 Definition
Lines that intersect in a single point.
Term
conditional statement
 Definition
A statement in the form "If p, then q," where p and q are declarative statements.
Term
congruent angles
 Definition
Angles that have the same measure.
Term
congruent arcs
 Definition
Arcs that have the same measure and are parts of the same circle or congruent circles.
Term
congruent segments
 Definition
Segments that have the same length.
Term
congruent triangles
 Definition
Triangles in which all pairs of corresponding parts (angles and sides) are congruent.
Term
construction
 Definition
A drawing made with only a compass and a straightedge.
Term
contrapositive
 Definition
A statement associated with a conditional statement "If p, then q," having the form "If not q, then not p."
Term
converse
 Definition
A statement associated with a conditional statement "If p, then q," having the form "If q, then p."
Term
convex polygon
 Definition
A polygon in which each interior angle has a measure less than 180 degrees.
Term
coplanar
 Definition
Lying in the same plane.
Term
corresponding angles
 Definition
In a figure formed by two lines and a transversal, a pair of angles on the same side of the transversal, one in the interior and one in the exterior of the figure, having different vertices.
Term
cross section
 Definition
The intersection of a solid with a plane.
Term
cyclic quadrilateral
 Definition
A quadrilateral that can be inscribed in a circle.
Term
diagonal (of a polygon)
 Definition
A segment that joins two nonconsecutive (nonadjacent) vertices of a polygon.
Term
diagonal (of a rectangular solid)
 Definition
A segment whose endpoints are vertices not in the same face of a rectangular solid.
Term
diameter
 Definition
A chord that passes through the center of a circle.
Term
distance
 Definition
The length of the shortest path between two objects.
Term
equiangular
 Definition
Having all angles congruent.
Term
equilateral
 Definition
Having all sides congruent.
Term
exterior angle
 Definition
An angle that is adjacent to and supplementary to an interior angle of a polygon.
Term
extremes
 Definition
The first and fourth terms of a proportion. In the proportion a:b=c:d, for example, a and d are these.
Term
face
 Definition
One of the polygonal surfaces making up a polyhedron.
Term
foot (of line)
 Definition
The point of intersection of a line and a plane.
Term
fourth proportional
 Definition
The fourth term of a proportion. In the proportion a:b=c:x, for example, x is this.
Term
frustum
 Definition
The portion of a pyramid or a cone that lies between the base and a cross section of the figure.
Term
geometric mean
 Definition
Either of the two means of a proportion in which the means are equal. Also called a mean proportional.
Term
hypotenuse
 Definition
The side opposite the right angle in a right triangle.
Term
hypothesis
 Definition
The "if" clause in a conditional statement.
Term
incenter
 Definition
A point associated with a polygon, corresponding to the center of the polygon's inscribed circle. (The incenter of a triangle is the point of concurrency of the triangle's angle bisectors.)
Term
inscribed angle
 Definition
An angle whose vertex is on a circle and whose sides are determined by two chords.
Term
inscribed polygon
 Definition
A polygon each of whose vertices lies on a circle.
Term
inverse
 Definition
A statement associated with a conditional statement "If p, then q," having the form "If not p, then not q."
Term
isosceles trapezoid
 Definition
A trapezoid in which the nonparallel sides are congruent.
Term
isosceles triangle
 Definition
A triangle in which at least two sides are congruent.
Term
kite
 Definition
A quadrilateral in which two disjoint pairs of consecutive sides are congruent.
Term
lateral surface area
 Definition
The sum of the areas of a solid's lateral faces.
Term
leg (of isosceles trapezoid)
 Definition
One of the nonparallel, congruent sides of an isosceles trapezoid.
Term
leg (of isosceles triangle)
 Definition
One of the two congruent sides of a nonequilateral isosceles triangle.
Term
leg (of right triangle)
 Definition
One of the sides that form the right angle in a right triangle.
Term
locus
 Definition
A set consisting of all the points, and only the points, that satisfy specific conditions.
Term
major arc
 Definition
An arc whose points or on or outside a central angle.
Term
means
 Definition
The second and third terms of a proportion. In the proportion a:b=c:d, for example, b and c are these.
Term
median (of trapezoid)
 Definition
A segment joining the midpoints of the nonparallel sides of a trapezoid.
Term
median (of triangle)
 Definition
A segment from a vertex of a triangle to the midpoint of the opposite side.
Term
midpoint
 Definition
A point that divides a segment or an arc into two congruent parts.
Term
minor arc
 Definition
An arc whose points are on or between the sides of a central angle.
Term
oblique lines
 Definition
Two intersecting lines that are not perpendicular.
Term
obtuse angle
 Definition
An angle whose measure is greater than 90 and less than 180 (degrees).
Term
opposite rays
 Definition
Two collinear rays that have a common endpoint and extend in opposite directions.
Term
orthocenter
 Definition
The point of concurrency of the altitudes of a triangle.
Term
parallel lines
 Definition
Coplanar lines that do not intersect.
Term
parallelogram
 Definition
A quadrilateral in which both pairs of opposite sides are parallel.
Term
perimeter
 Definition
The sum of the lengths of the sides of a polygon.
Term
perpendicular
 Definition
Intersecting at right angles.
Term
perpendicular bisector
 Definition
A line that bisects and is perpendicular to a segment.
Term
plane
 Definition
A surface such that if any two points on the surface are connected by a line, all points of the line are also on the surface.
Term
postulate
 Definition
An unproved assumption.
Term
prism
 Definition
A solid figure that has two congruent parallel faces whose corresponding vertices are joined by parallel edges.
Term
proportion
 Definition
An equation stating that two or more ratios are equal.
Term
protractor
 Definition
An instrument, marked in degrees, used to measure angles.
Term
pyramid
 Definition
A solid figure that has a polygonal base and lateral edges that meet in a single point.
Term
quadrilateral
 Definition
A four-sided polygon.
Term
radius (of circle)
 Definition
A segment joining the center of a circle to a point on the circle. Also, the length of such a segment.
Term
radius (of regular polygon)
 Definition
A segment joining the center of a regular polygon to one of the polygon's vertices.
Term
ratio
 Definition
A quotient of two numbers.
Term
ray
 Definition
A straight set of points that begins at an endpoint and extends infinitely in one direction.
Term
rectangle
 Definition
A parallelogram in which at least one angle is a right angle.
Term
rectangular solid
 Definition
A prism with six rectangular faces.
Term
regular polygon
 Definition
A polygon that is both equilateral and equiangular.
Term
rhombus
 Definition
A parallelogram in which at least two consecutive sides are congruent.
Term
right angle
 Definition
An angle whose measure is 90 degrees.
Term
right triangle
 Definition
A triangle in which one of the angles is a right angle.
Term
scalene triangle
 Definition
A triangle in which no two sides are congruent.
Term
secant
 Definition
A line that intersects a circle at exactly two points.
Term
secant-secant angle
 Definition
An angle whose vertex is outside a circle and whose sides are determined by two secants.
Term
secant segment
 Definition
The part of a secant that joins a point outside the circle to the farther point of intersection of the secant and the circle.
Term
secant-tangent angle
 Definition
An angle whose vertex is outside a circle and whose sides are determined by a secant and a tangent.
Term
sector
 Definition
A region bounded by two radii and an arc of a circle.
Term
segment (of circle)
 Definition
A region bounded by a chord of a circle and its corresponding arc.
Term
semicircle
 Definition
An arc whose endpoints are the endpoints of a diameter.
Term
similar polygons
 Definition
Polygons in which the ratios of the measures of corresponding sides are equal and corresponding angles are congruent.
Term
skew lines
 Definition
Two lines that are not coplanar.
Term
slant height
 Definition
A perpendicular segment from the vertex of a pyramid to a side of the pyramid's base.
Term
square
 Definition
A parallelogram that is both a rhombus and a rectangle.
Term
straight angle
 Definition
An angle whose measure is 180 degrees.
Term
supplementary angles
 Definition
Two angles whose sum is 180 degrees (a straight angle).
Term
tangent
 Definition
A line that intersects a circle at exactly one point.
Term
tangent-chord angle
 Definition
An angle whose vertex is on a circle and whose sides are determined by a tangent and a chord that intersect at the tangent's point of contact.
Term
tangent circles
 Definition
Circles that intersect at exactly one point.
Term
tangent segment
 Definition
The part of a tangent line between the point of contact and a point outside the circle.
Term
tangent-tangent angle
 Definition
An angle whose vertex is outside a circle and whose sides are determined by two tangents.
Term
theorem
 Definition
A mathematical statement that can be proved.
Term
transversal
 Definition
A line that intersects two coplanar lines in two distinct points.
Term
trapezoid
 Definition
A quadrilateral with exactly one pair of parallel sides.
Term
triangle
 Definition
A three-sided polygon.
Term
trisect
 Definition
To divide a segment or an angle into three congruent parts.
Term
vertex (of angle)
 Definition
The common endpoint of the two rays that form an angle.
Term
vertex (of polygon)
 Definition
The common endpoint of two sides of a polygon.
Term
vertex angle
 Definition
The angle opposite the base of a nonequilateral isosceles triangle.
Term
vertical angles
 Definition
A pair of angles such that the rays forming the sides of one and the rays forming the sides of the other are opposite rays.
Term
volume
 Definition
The number of cubic units of space contained by a solid figure.
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