PARALLEL AND PERPENDICULAR POSTULATES

Relationship between Lines

Two lines are parallel lines, if they are coplanar and do not intersect. Lines that do not intersect and are not coplanar are called skew lines. Similarly, two planes that do not intersect are called parallel planes.  

When two lines AB and CD are parallel, we can write it as AB||CD. Triangles like those AB and CD are used on diagrams to indicate that lines are parallel. Segments and rays are parallel if they lie on parallel lines. 

For example, AB||CD. 

Parallel Postulate

If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line.  

The diagram given below illustrates this.

The fifth postulate of Euclidean Geometry states that through any given point not on a line there passes exactly one line parallel to that line in the same plane. This is called Parallel Postulate.  

Perpendicular Postulate

If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line.  

The diagram shown below below illustrates this.

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