Angles in Parallel Lines

What is it?

When a transversal (a straight line) crosses two parallel lines, it creates different types of angles. Some of these angles are equal, and others add up to 180°.

|AB| and |CD| are parallel lines.

|PS| is transversal lines.

Types

1. Corresponding Angles:

These are in the same position on both sides of the transversal.
They are always equal.

2. Alternate Angles

These sit on opposite sides of the transversal, but between the two parallel lines.
They are also equal.

**Top Tip:Look for a “Z” shape – the angles inside the corners of the Z are alternate and equal.**

3. Allied Angles (also called co-interior or supplementary angles)

These are on the same side of the transversal and inside the parallel lines.
They add up to 180°.

**Top Tip:Look for a “C” shape – these two angles always add to 180°.**

4.Vertically Opposite Angles

These are formed when two lines cross.
They are always equal.

Top Tip:Think of a pair of scissors – the angles on opposite sides are the same! — **Top Tip:**Think of a pair of scissors – the angles on opposite sides are the same!

Top Tips:

Angle Type	Rule	Tip
Corresponding	Equal angles	Same place, F shape
Alternate	Equal angles	Z shape, opposite sides
Allied (Co-interior)	Add to 180°	C shape, same side
Vertically Opposite	Equal angles	Cross shape, opposite sides