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20 terms

NHS Honors Geometry Chap 1

STUDY
PLAY
point
A point has no dimension. It is represented by a dot.
line
A line has one dimension. It is represented by a line with two arrowheads (↔), but it extends without end. Through any two points, there is exactly one line. You can use any two points on a line to name it.
plane
A plane has two dimensions. It is represented by a shape that looks like a floor or a wall, but it extends without end. Through any three points not on the same line, there is exactly one plane. You can use three points that are not all on the same line to name a plane.
undefined terms
Words that do not have formal definitions, but there is agreements about what they mean. Point, line, and plane are all examples.
collinear points
points that lie on the same line.
coplanar points
points that lie on the same plane.
defined terms
Terms that can be described using known words such as point or line.
line segment (or segment)
(written with a line, − , over AB) consists of the endpoints A and B and all points on line AB that are between A and B. Line segment AB can also be named line segment BA.
ray
(written with an arrow, →, over AB) consists of the endpoint A and all points on line AB that line on the same side of A as B. Ray AB and Ray BA are DIFFERENT rays.
opposite rays
If point C lies on line AB between A and B, then ray CA and ray CB are opposite rays. Opposite rays are collinear.
intersection
The set of points the geometric figures have in common, when two or more geometric figures intersect.
postulate (axiom)
a rule that is accepted without proof.
Ruler Postulate
Disntance between points A and B, written as AB, is the absolute value of the difference of the coordinates of A and B. AB = |x₂ - x₁|
between
Point B is between point A and point C iff (if and only if) point B is collinear to point A and point C.
Segment Addition Postulate
If B is between A and C, then AB + BC = AC. If AB + BC = AC, then B is between A and C.
Congruent segments
Line segments that have the same length.
Midpoint
The point that divides the segment into two congruent segments.
Segment bisector
A point, ray, line, line segment, or plane that intersects the segment at its midpoint.
Midpoint Formula
The coordinates of the midpoint of a segment are the averages of the x-coordinates and of the y-coordinates of the endpoints. If A (x₁, y₁) and B (x₂, y₂) are points in a coordinate plane, then the midpoint M of segment AB has coordinates: [(x₁+x₂)/2 , (y₁+y₂)/2]
Distance Formula
If A (x₁, y₁) and B (x₂, y₂) are points in a coordinate plane, then the distance between A and B is
AB=√(x₂-x₁) + (y₂ - y₁)