# Chapter 1 = distant, Planes, Segments, Angles, Postulates + Theorems

Equally distant. Equidistant
A location that has no length, width, and thickness. (Labeled + named with capital letter) Point
An infinite set of points that extends in two directions. (Named by lowercase letter or two points on line) Line
An infinite set of points that creates a flat surface and extends without ending. (Named by capital letter or vertices) Plane
A plane that has its two longest sides going left and right. Horizontal plane
A plane that has its two longest sides going up and down. Vertical plane
The set of all points. Space
Points on the same line. Collinear
Points not on the same line. Noncollinear
Points in the same plane. Coplanar
Points not in the same plane. Noncoplanar
The set of points in both figures. Intersection
This is named by giving its endpoints. Segment
This is named by giving its endpoint and another point on it. (Endpoint always comes first) Ray
Rays that share a common endpoint, but go off in opposite directions. Opposite rays
Another word for distance. Length
The length of a segment on a number line can be found by finding the absolute value of the difference of its endpoints' coordinates. The length must be positive. Ruler Postulate
If point B is between points A and C on segment AC, then the segment AB added to the segment BC can get you the length of segment AC. Segment Addition Postulate
Having the same size and shape. Congruent
This divides a segment into two congruent segments. Midpoint of a segment
A line, segment, ray, or plane that intersects a segment at its midpoint. Bisector of a segment
A figure formed by two rays with the same endpoint. Angle
The two rays that make and angle. Sides of an angle
The point where the two rays meet to make an angle. Vertex of an angle
The degrees of an angle. Measure of an angle
You can find the measure in degrees of an angle by using a protractor to find the absolute value of the difference of the sides of the angle. Protractor Postulate
An angle that is greater than 0 and less than 90. Acute angle
An angle that is greater than 90 and less than 180. Obtuse angle
An angle that is exactly 90 degrees. Right angle
An angle that is exactly 180 degrees. Straight angle
If a point D lies in the interior of an angle ABC, then the measure of angle ABD added to the measure of angle DBC is the measure of angle ABC. Angle Addition Postulate
Two angles with equal measures. Congruent angles
The ray that divides an angle into two congruent angles. Bisector of an angle
Coplanar angles with a common vertex and a common side, but no common interior points. Adjacent angles
A basic assumption accepted without proof. Postulate
A statement that can be proved using postulates, definitions, and previously proved versions of this. Theorem
There is at least one. Exists
There is no more than one. Unique
Exactly one. One and only one
To define or specify. Determine
Two relationships between two lines in the same plane. Parallel or intersect at one point
Three relationships between a line and a plane. Parallel, intersect at one point, or plane contains line
Two relationships between two planes. Parallel or intersect in a line
A line contains at least two points; a plane contains at least three noncollinear points; space contains at least four noncoplanar points. Postulate 5
Through any two points there is exactly one line. Postulate 6
Through any three points there is at least one plane, and through any three noncollinear points there is exactly one plane. Postulate 7
If two points are in a plane, then the line that contains the points is in that plane. Postulate 8
If two planes intersect, then their intersection is a line. Postulate 9
If two lines intersect, then they intersect in exactly one point. Theorem 1-1
Through a line and a point not in the line there is exactly one plane. Theorem 1-2
If two lines intersect, then exactly one plane contains the lines. Theorem 1-3