1-1 Understanding Points, Lines, and Planes
Which postulate explains the fact that two straight roads cannot cross each other more than once?
1-1-4
A plane
A flat surface that has no thickness and extends forever. Notation: A script capital letter or three noncollinear points.
Endpoint
A point at one end of a segment or the starting point of a ray.
Postulate or axiom
A statement that is accepted as true without proof.
A line
A straight path that has not thickness and extends forever. Notation: a lower case letter, or 2points with line above.
Name all possible lines, segments, and rays for the points A and B. Give the maximum number of planes that can be determined by these points.
AB, AB, AB, BA; 0 planes
Why are any two points collinear?
By Postulate 1-1-1, through any two points there is a line. Any two points are collinear.
Postulate 1-1-4
If two lines intersect, then they intersect in exactly one point.
Postulate 1-1-5
If two planes intersect, then they intersect in exactly one line.
Postulate 1-1-3
If two points lie in a plane, then the line containing those points lies in the plane.
A Point
Names a location and has no size. It is represented by a dot. Notation: Capital letter ( P)
A segment
Part of a line consisting of two points and all the points between them. Notation: Endpoints with a segment on top.
A ray
Part of a line that starts at an endpoint and extends forever in one directon. Notation: Endpont and directional point with a little ray on top.
Coplanar
Points that lie in the same plane .
Collinear
Points that lie on the same line.
Undefined terms
Terms which cannot be defined by using other figures. Point, Line and Plane are the building blocks of geometry.
Postulate 1-1-2
Through any three noncollinear points there are exactly one plane containing them.
Postulate 1-1-1
Through any two points there is exactly one line.
Opposite rays
Two rays that have a common endpoint and form a line.
What are the building blocks of geometry?
point, line, and plane