Only when the lines are parallel

A bamboo ladder has two side poles and rungs across them. What if the poles are not parallel?

The rule

If the poles are not parallel, the facts below fail.

On parallel lines, a corresponding pair is equal. So is an alternate pair. A co-interior pair adds to 180°.

It works backwards too. An equal corresponding or alternate pair means the lines are parallel. A co-interior pair that adds to 180° means the same.

Each fact needs the lines to be parallel. A pair on lines that are not parallel misses by some amount. That amount is the angle between the lines.

A one-degree tilt is hard to see. The lines cross far past the page edge. Looking may not show a tilt. Careful angle measuring can.

Tilt the lower line by one degree. Watch the pair.

Try the lab to finish this lesson.