We've already looked at some angle relationships on parallel lines. Just to recap:
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 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.
Are the lines $AB$AB and $CD$CD parallel?
$AB$AB and $CD$CD are not parallel because:
Deduce the angle properties of intersecting and parallel lines and the angle properties of polygons and apply these properties