Lines and Angles

Lines and Angles Types and Properties

Parallel lines
Two lines are parallel, if
They are in the same plane and
Do not intersect

The distance between two parallel lines does not change. That is why these lines do not meet anywhere.

Transversal line

If two lines AB and CD, parallel or non-parallel, are cut by a third line PQ, then PQ is called a transversal line.

A transversal forms the following angles with the two given lines.
Exterior angles
Interior angles
Alternate angles
Corresponding
Exterior angles: Angles marked 1, 2, 7, and 8 are exterior angles.
Interior angles: Angles marked 3, 4, 5, and 6 are interior angles.
Alternate angles: Angles marked 3 and 6 or 4 and 5 are alternate angles.
Corresponding angles: Angles marked as 1 and 5;2 and 6; 3 and 7; 4 and 8; which are on the same side of the transversal PQ are called corresponding angles.

Properties of the Angles Formed by Parallel Lines and Transversal
If a transversal cuts two parallel lines then
Alternate angles are equal
The sum of the interior opposite angles on the same side of a transversal is 180º

Converse property is also true
If a transversal cuts two lines such that any of the following conditions are satisfied:
A pair of alternate angles are equal
A pair of corresponding angles are equal
The sum of the interior opposite, angles on the same side of the transversal is 180º, then the lines are parallel to each other.