We've seen angles crop up a few times now. Let's look at some common properties of angles on lines that intersect parallel lines
First, remember that an angle on a straight line, like in the image above, can be considered to be \(180^\circ\).
And when two lines cross, there are pairs of equal angles, as in the image bellow
So angles \(a\) and \(c\) are the same and angles \(b\) and \(d\) are the same. All four add up to \(360^\circ\).
When a line crosses through parallel lines, we get interesting properties. Look at the following diagram
Alternate interior angles, sometimes called Z-angles, are equal. In this image \(c\) and \(f\) are an equal pair of alternate interior angles. Can you find another pair?
Same side interior angles are supplementary - they add up to \(180^\circ\). In the image, \(c\) and \(e\) are a supplementary pair of same side interior angles. Can you find another pair?
Alternate exterior angles are equal. In the image, \(b\) and \(g\) are and equal pair of alternate exterior angles. Can you find another pair?
Same side exterior angles are supplementary. An example of same side exterior angles in the image are \(a\) and \(g\). Can you find another pair of same side exterior angles?
Corresponding angles are equal. An example of corresponding angles in the image are \(b\) and \(f\). Can you find another example of corresponding angles?