Vocabulary from Discovering Geometry sections 1.1 thru 1.7
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).
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.
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.
A statement that clarifies or explains the meaning of a word or phrase.
On the same line.
In the same plane.
Two points and all the points between them that are collinear with the two points.
The point at either end of a segment or arc, or the first point of a ray.
Two or more segments that have the same measure or length.
The point on a line segment that is the same distance from both endpoints.
The midpoint between (x1,y1) and (x2,y2) is found by using ( (x1+x2)/2 , (y1+y2)/2 )
To divide into two congruent parts.
A point on a line, and all the points of the line that lie on one side of this point.
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.
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.
Two or more angles that have the same measure.
A ray that has its endpoint at the vertex of the angle and that divides the angle into two congruent angles.
Two non-overlapping angles with a common vertex and one common side.
An example that shows a conjecture to be incorrect or a definition to be inadequate.
Lines that meet at 90° angles.
Lines that lie in the same plane and do not intersect.
Lines that are not in the same plane and do not intersect.
An angle whose measure is 90°.
An angle whose measure is less than 90°.
An angle whose measure is greater than 90°, but less than 180°.
Two angles whose measures have the sum 90°.
Two angles whose measures have the sum 180°.
Two nonadjacent angles formed by two intersecting lines.
linear pair (of angles)
Two adjacent supplementary angles whose non-common sides form a line.
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.
A polygon with 3 sides
A polygon with 4 sides
A polygon with 5 sides
A polygon with 6 sides
A polygon with 7 sides
A polygon with 8 sides
A polygon with 9 sides
A polygon with 10 sides
A polygon with 11 sides
A polygon with 12 sides
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.
A line segment connecting two nonconsecutive vertices of a polygon or polyhedron.
A polygon with no diagonal outside the polygon.
A polygon with at least one diagonal outside the polygon.
Two or more polygons with the exact same size and shape.
The length of the boundary of a two-dimensional figure. For a polygon it is the sum of the lengths of its sides.
A polygon whose sides are congruent.
A polygon whose angles are congruent.
A polygon that is both equilateral and equiangular.
To accept as true without facts or proof.
A triangle with a right angle.
A triangle with three acute angles.
A triangle with an obtuse angle.
A triangle with three sides of different lengths.
A triangle whose sides are congruent.
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.
The angle between the two congruent sides (of an isosceles triangle)
The side opposite the vertex angle. (of an isosceles triangle)
The two angles opposite the two congruent sides. (of an isosceles triangle)
A quadrilateral with exactly one pair of parallel sides
A quadrilateral with exactly two distinct pairs of congruent consecutive sides.
A quadrilateral in which both pairs of opposite sides are parallel.
An equilateral parallelogram.
An equiangular parallelogram.
An equiangular rhombus, an equilateral rectangle, a regular quadrilateral.
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.
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.
A line segment whose endpoints lie on a circle.
A chord of a circle that contains the center, or the length of that chord.
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.
Two or more circles with the same radius.
Circles that share the same center.
Two points on a circle and the continuous part of the circle between them.
An arc of a circle whose endpoints are the endpoints of a diameter. An arc whose degree measure is 180°.
An arc of a circle that is less than a semicircle.
An arc of a circle that is greater than a semicircle.
The measure of the central angle that intercepts an arc, measured in degrees.
An angle whose vertex is the center of a circle and whose sides pass through the endpoints of an arc.