Point and plane

Point:

A point is that which has no part. A point is represented by a fine dot made by a sharp pencil on a sheet of paper.

Plane:

The surface of a smooth wall or the surface of a sheet of paper or the surface of a smooth black board is close examples of a plane.

Plane

Line:

A line is breadth less length e.g., the edge of a ruler, the edge of the top of a table, the meeting place of two walls of a room is also examples of a geometrical straight line.

straight line

Collinear Points:

·    Three or more points are said to be collinear, if there is a line that contains all of them.

Collinear Points

 

Concurrent Lines:

·       Three or more lines are said to be concurrent, if all of them pass through a common point.

·         Two distinct lines cannot have more than one point in common.

Concurrent Lines

 

Intersecting Lines:

·Two lines who meet at one point are said to be intersecting lines. The common point is called the ‘point of intersection’.

Intersecting Lines

Parallel Lines:

· Two lines l and m in a plane are said to be parallel lines, if  l Ç m = f . If  l and m are parallel lines in a plane then denote as  l ||  .

Parallel Lines

·                     Two lines which are both parallel to the other line then all lines are parallel to each other.

·                     If l, m, n are lines in the same plane such that l intersects m and n || m, then l intersects n also.

·                     If l and m are intersecting line, l || p and q || m, then p and q also intersect.

 

Intercept Theorem:

·  If a transversal makes equal intercepts on three or more parallel lines, any other line cutting them will also make equal intercepts.

 Hence,                  AC/CE = BD/DF

Intercept Theorem