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Learn about segments, rays, angles, and postulates in geometry. Understand concepts like distance, midpoint, congruence, and more.
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Segment: The set of points consisting of two points called endpoints and all the points between these points
Sides of an angle • The rays of an angle
Vertex • The common endpoint of the sides of an angle
Distance: The absolute value of the difference of the coordinates for any two points on a number line
Ray: that A ray, is the part of that contains point A and all points on the same side of A as B
Opposite Rays • Rays that have the same endpoint and that together make a line.
Postulate (or axiom): A statement that is accepted as true without proof
Congruent: Figures that have the same size and shape
Congruent segments: Segments that have the same length
Midpoint of a segment: The point that divides the segment into two congruent segments
Bisector of a segment: A line, segment, ray, of plane that intersects the segment at its midpoint
Postulate 1 • Ruler Postulate • 1. The points on a line can be paired with the real numbers in such a way that any two points can have coordinates 0 and 1. • 2. Once a coordinate system has been chosen in this way, the distance between any two points equals the absolute value of the difference of their coordinates.
Postulate 2: Segment Addition Postulate If B is between A and C, then AB+BC=AC