# Parallel Lines

## What are Parallel Lines?

Non-intersecting straight lines, which do not meet when produced however far on either side, are called ‘parallel’.

The distance between the parallel lines *AB* and *CD* is the length of the perpendicular *PQ* from *P* (any point in *AB*) to *CD*.

The distance between any two parallel lines will always remain the same. A line is parallel to itself. Through a given point, only one straight line can be drawn parallel to another straight line.

A ‘transversal’ is a straight line which cuts two or more straight lines.

The pair of angles 1 and 5, 2 and 6, 3 and 7, 4 and 8 are called ‘corresponding angles’.

The pair of angles 3 and 5, 4 and 6 are called ‘alternate angles’.

*Example*: Find the value of *x*.

10*x* + 5 = 65° (corresponding angles)

10*x* + 5 – 5 = 65° – 5

10*x* = 60°

= => *x* = 6

### CHECK POINT

- What is the measure of the indicated angle?

2. Solve for *x*:

### True or False:

When a transversal cuts two parallel lines, then the pairs of corresponding angles so formed are equal. __________

1. Solve for *x*:

2. Find the value of *x*:

##### Answer key

- 78°
- 9
- True
- 6
- 8

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