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point

An undefined term thought of as a location with no size or dimension. It is the most basic building block of geometry. In a two-dimensional coordinate system, its location is represented by an ordered pair of numbers (x, y).

line

An undefined term thought of as a straight, continuous arrangement of infinitely many points extending forever in two directions. It has length, but no width or thickness, so it is one-dimensional.

plane

An undefined term thought of as a flat surface that extends infinitely along its edges. It has length and width but no thickness, so it is two-dimensional.

definition

A statement that clarifies or explains the meaning of a word or phrase.

collinear

On the same line.

coplanar

In the same plane.

line segment

Two points and all the points between them that are collinear with the two points.

endpoint

The point at either end of a segment or arc, or the first point of a ray.

congruent segments

Two or more segments that have the same measure or length.

midpoint

The point on a line segment that is the same distance from both endpoints.

Midpoint Formula

The midpoint between (x1,y1) and (x2,y2) is found by using ( (x1+x2)/2 , (y1+y2)/2 )

bisect

To divide into two congruent parts.

ray

A point on a line, and all the points of the line that lie on one side of this point.

angle

Two non-collinear rays having a common endpoint

vertex (of an angle)

The common endpoint of the two rays of the angle.

side (of an angle)

One of the two rays that form an angle.

measure of an angle

The smallest amount of rotation about the vertex from one ray to the other, measured in degrees.

degree

A unit of measure for angles and arcs equivalent to 1/360 of a rotation around a circle.

protractor (or geometer)

A tool used to measure the size of an angle in degrees.

congruent angles

Two or more angles that have the same measure.

angle bisector

A ray that has its endpoint at the vertex of the angle and that divides the angle into two congruent angles.

adjacent angles

Two non-overlapping angles with a common vertex and one common side.

counterexample

An example that shows a conjecture to be incorrect or a definition to be inadequate.

perpendicular

Lines that meet at 90° angles.

parallel

Lines that lie in the same plane and do not intersect.

skew lines

Lines that are not in the same plane and do not intersect.

right angle

An angle whose measure is 90°.

acute angle

An angle whose measure is less than 90°.

obtuse angle

An angle whose measure is greater than 90°, but less than 180°.

complementary angles

Two angles whose measures have the sum 90°.

supplementary angles

Two angles whose measures have the sum 180°.

vertical angles

Two nonadjacent angles formed by two intersecting lines.

linear pair (of angles)

Two adjacent supplementary angles whose non-common sides form a line.

polygon

A closed figure in a plane, formed by connecting line segments endpoint to endpoint with each segment intersecting exactly two others.

side (of a polygon)

A line segment connecting consecutive vertices of a polygon.

vertex (of a polygon)

An endpoint where two sides of the polygon meet.

angle (of a polygon)

An angle having two adjacent sides of the polygon as its sides.

triangle

A polygon with 3 sides

quadrilateral

A polygon with 4 sides

pentagon

A polygon with 5 sides

hexagon

A polygon with 6 sides

heptagon

A polygon with 7 sides

octagon

A polygon with 8 sides

nonagon

A polygon with 9 sides

decagon

A polygon with 10 sides

undecagon

A polygon with 11 sides

dodecagon

A polygon with 12 sides

n-gon

A polygon with n sides.

consecutive (angles, sides or vertices of a polygon)

Two angles that share a common side, two sides that share a common vertex, or two vertices that are the endpoints of one side.

diagonal

A line segment connecting two nonconsecutive vertices of a polygon or polyhedron.

convex polygon

A polygon with no diagonal outside the polygon.

concave polygon

A polygon with at least one diagonal outside the polygon.

congruent polygons

Two or more polygons with the exact same size and shape.

perimeter

The length of the boundary of a two-dimensional figure. For a polygon it is the sum of the lengths of its sides.

equilateral polygon

A polygon whose sides are congruent.

equiangular polygon

A polygon whose angles are congruent.

regular polygon

A polygon that is both equilateral and equiangular.

assume

To accept as true without facts or proof.

right triangle

A triangle with a right angle.

acute triangle

A triangle with three acute angles.

obtuse triangle

A triangle with an obtuse angle.

scalene triangle

A triangle with three sides of different lengths.

equilateral triangle

A triangle whose sides are congruent.

isosceles triangle

A triangle with at least two congruent sides. Note : Most have only two congruent sides, although an equilateral triangle can be considered one as well.

vertex angle

The angle between the two congruent sides (of an isosceles triangle)

base

The side opposite the vertex angle. (of an isosceles triangle)

base angles

The two angles opposite the two congruent sides. (of an isosceles triangle)

trapezoid

A quadrilateral with exactly one pair of parallel sides

kite

A quadrilateral with exactly two distinct pairs of congruent consecutive sides.

parallelogram

A quadrilateral in which both pairs of opposite sides are parallel.

rhombus

An equilateral parallelogram.

rectangle

An equiangular parallelogram.

square

An equiangular rhombus, an equilateral rectangle, a regular quadrilateral.

circle

The set of all points in a plane at a given distance from a given point.

center (of a circle)

The coplanar point from which all points of the circle are the same distance.

radius

A line segment from the center of a circle or sphere to a point on the circle or sphere. Also, the length of that line segment.

chord

A line segment whose endpoints lie on a circle.

diameter

A chord of a circle that contains the center, or the length of that chord.

tangent line

A line that lies in the plane of a circle and that intersects the circle at exactly one point.

point of tangency

The point of intersection of a tangent line and a circle.

congruent circles

Two or more circles with the same radius.

concentric circles

Circles that share the same center.

arc

Two points on a circle and the continuous part of the circle between them.

semicircle

An arc of a circle whose endpoints are the endpoints of a diameter. An arc whose degree measure is 180°.

minor arc

An arc of a circle that is less than a semicircle.

major arc

An arc of a circle that is greater than a semicircle.

arc measure

The measure of the central angle that intercepts an arc, measured in degrees.

central angle

An angle whose vertex is the center of a circle and whose sides pass through the endpoints of an arc.