Points, lines and planes
Line
A line has only one dimension: length. It continues forever in two directions (so it has infinite length), but it has no width at all. A line connects two points via the shortest path, and then continues on in both directions.
Linear pair
A linear pair of angles is formed when two lines intersect. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines. The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.
Space
A linear space is a basic structure in incidence geometry. A linear space consists of a set of elements called points, and a set of elements called lines. Each line is a distinct subset of the points.
Plane
A plane is a flat, two-dimensional object. We often represent a plane by a piece of paper, a blackboard, or the top of a desk. In fact, none of these is actually a plane, because a plane must continue infinitely in all directions and have no thickness at all. A plane can be defined by two intersecting lines or by three non-collinear points.
Point
A point specifies only location; it has no length, width, or depth. We usually represent a point with a dot on paper, but the dot we make has some dimension, while a true point has dimension 0.
Opposite ray
A ray has one endpoint and extends indefinitely in one direction. A pair of opposite rays are two rays that have the same endpoint and extend in opposite directions. Rays are always named with two points and the first point in the name must be the endpoint.
Interior
An Interior Angle is an angle inside a shape.
Angles
Angles can be either straight, right, acute or obtuse. An angle is a fraction of a circle where the whole circle is 360°. A straight angle is the same as half the circle and is 180° whereas a right angle is a quarter of a circle and is 90°. You measure the size of an angle with a protractor.
Congruent angles
Congruent Angles have the same angle (in degrees or radians). That is all. They don't have to point in the same direction. They don't have to be on similar sized lines.
Congruent segments
Congruent segments are simply line segments that are equal in length. Congruent means equal. Congruent line segments are usually indicated by drawing the same amount of little tic lines in the middle of the segments, perpendicular to the segments. We indicate a line segment by drawing a line over its two endpoints.
Segment
In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints. A closed line segment includes both endpoints, while an open line segment excludes both endpoints; a half-open line segment includes exactly one of the endpoints.
Ray
In geometry, a ray is a line with a single endpoint (or point of origin) that extends infinitely in one direction
Vertex
In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra are vertices.
Segment addition postulate
In geometry, the segment addition postulate states that given two points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.
Non-coplanar
Lines that do not lie on the same surface or plane are non-coplanar.
Non-collinear
Points that do not all lie on a single line.
Collinear
Points that lie on the same straight line
Segment bisector
Segment Bisector: A point, segment, line, or plane that divides a line segment into two equal parts. The bisector of a segment always contains the midpoint of the segment
Angle addition postulate
The Angle Addition Postulate states that: If point B lies in the interior of angle AOC, then. . The postulate describes that putting two angles sides-by-side with their vertices together creates a new angle whose measure equals the sum of the measures of the two original angles.
Exterior
The Exterior Angle is the angle between any side of a shape, and a line extended from the next side.
Acute angles
The acute angle is the small angle which is less than 90°. If you choose the larger angle you. will have a Reflex Angle instead: The smaller angle is an Acute Angle, but the larger angle is a Reflex Angle.
Distance between two points
The distance formula is derived from the Pythagorean theorem. To find the distance between two points
Obtuse angles
The obtuse angle is the smaller angle. It is more than 90° and less than 180°. The smaller angle is an Obtuse Angle, but the larger angle is a Reflex Angle.
Midpoint
The point halfway between the endpoints of a line segment is called the midpoint. A midpoint divides a line segment into two equal segments. By definition, a midpoint of a line segment is the point on that line segment that divides the segment two congruent segments.
Adjacent angles
Two angles are Adjacent when they have a common side and a common vertex (corner point) and don't overlap.
Betweenness of points
a point is between two other points on the same line iff its coordinate is between their coordinates
Right angle
an angle of 90°, as in a corner of a square or at the intersection of two perpendicular straight lines.
Vertical angles
each of the pairs of opposite angles made by two intersecting lines.
Supplementary angles
either of two angles whose sum is 180°.
Complementary angles
either of two angles whose sum is 90°.
Coplanar
in the same plane.
Angle bisector
the angle bisector theorem is concerned with the relative lengths of the two segments that a triangle's side is divided into by a line that bisects the opposite angle. It equates their relative lengths to the relative lengths of the other two sides of the triangle.
Perpendicular lines
the property of being perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees). The property extends to other related geometric objects. A line is said to be perpendicular to another line if the two lines intersect at a right angle.
