Parallel lines - Definition:

Two lines are said to be parallel, if they are in the same distance away at each point.

• That is, two lines are said to be parallel if
• They both lie in the same plane and
• They do not intersect (or cross each other)
• The above definition really means that parallel lines never cross each other.

What is a transversal?

A line that crosses a pair of parallel lines on a slant is called as the transversal line. Totally eight angles are formed as the transversal line crosses the parallel lines. In the 8 angles, one can observe that 4 of them are quite large whereas remaining 4 of them are quite small.

A very important set of properties of these angles is that the angles which appear to be same really are exactly the same. Therefore,

1 = 3 = 5 = 7

And

2 = 4 = 6 = 8

1 + 2 = 2 + 3 = 3 + 4 = 5 + 6 = 180degrees ( Pairs of adjacent angles always sum up to 180 degrees)

The following are the properties of parallel lines that should be understood properly:

• 1 and 5, 4 and 8, 2 and 6 and 3 and 7 are corresponding angles. That is, angles in the same relative position around the two intersection points are called corresponding angles.
• 1 and 7 and 2 and 8 are called alternate interior angles. Therefore, alternate interior angles are equal.
• 4 and 6 and 3 and 5 are called alternate exterior angles. Therefore, alternate exterior angles are equal.

The above properties are very important for understanding and exploiting the properties of similar triangles.

The above properties work in both the ways. For example, all it takes to find 2 lines are parallel is to show that when a transversal is drawn, one of the corresponding angles formed will be equal.