Identifying Parallel Lines

We've already looked at some angle relationships on parallel lines. Just to recap:

• Corresponding angles on parallel lines are equal.
• Alternate angles on parallel lines are equal.
• Co-interior angles inside parallel lines are equal.

We have mainly used these rules to find the values of angles. However, we can also use these angle relationships to prove whether or not lines are parallel. To do this , we use the rules in reverse.

We can say:

• If two corresponding angles are equal, then the two lines that the transversal cross are parallel.
• If two alternate angles are equal, then the two lines that the transversal cross are parallel.

• If two co-interior angles add up to $180^\circ$180°, then the two lines that the transversal cross are parallel.

 

Let's look through some examples and see if you can determine whether or not the lines are parallel.

 

Examples

Question 1

Are the lines $AB$AB and $CD$CD parallel?

 

Question 2

$AB$AB and $CD$CD are not parallel because: