Postulates and Theorems involving Points, Lines, and Planes Flashcards
P1
. Given any two distinct points, there is exactly one line that contains them.
P2.
Every line contains at least two distinct points.
P3.
(The Distance Postulate) To every pair of distinct points there corresponds a unique positive number. This number is called the distance between the two points.
P4.
(The Ruler Postullate) The points of a line can be placed in a correspondence with the real numbers such that
(a) To every point of the line there corresponds exactly one real number.
(b) To every real number there corresponds exactly one point of the line.
(c) The distance between two distinct points is the absolute value of the difference of the corresponding real numbers.
P6.
(Segment Addition Postulate) If B is between A and C, then AB+BC = AC
P5.
(The Ruler Placement Postulate) Given two points P and Q of a line,
the coordinate system can be chosen in such a way that the coordinate of P is zero and the coordinate of Q is positive.
P7.
(a) Every plane contains at least three non-collinear points.
(b) Space contains at least four non-coplanar points..
PB.
If two points lie in a plane, then the line containing these points lies in the same plane.
P9.
Any three points lie in at least one plane, and any three non-collinear points lie in exactly one plane
P10.
If two planes intersect, then their intersection is a line.
From the above postulates, we can also draw some theorems, without proof, about points, lines and planes.
T3.
If two distinct lines intersect, then exactly one plane contains both lines.
T1.
If two different lines intersect, then they intersect at exactly one point.
T2.
If a point lies outside a line, then exactly one plane contains both the line and the point
