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