Parallel lines: cheat sheet

Angles and shapes · The words and methods from the lessons, with an example of each.

transversal

Parallel lines go the same way and never meet; arrows (>>) mark them. A transversal crosses both, making eight angles.

\text{parallel lines} \gg \text{ crossed by a transversal}

alternate angles

Between the parallel lines, on opposite sides of the transversal (a Z shape). With parallel lines they are equal.

c = f

c and f: between the lines, opposite sides, both 60°

vertically opposite angles

Opposite each other at one crossing: always equal, parallel lines or not. Not one of the parallel-line pairs.

b = c

give a reason

For each angle you find, name the rule: corresponding or alternate angles are equal; co-interior angles add to $180^\circ$ ; angles on a straight line add to $180^\circ$ .

f = 70^\circ \;\text{(corresponding to } b\text{)}

corresponding angles

The same place at each crossing (an F shape). With parallel lines they are equal.

a = e

a and e: the same place at each crossing, both 120°

co-interior angles

Between the parallel lines, on the same side (a C shape). With parallel lines they add to $180^\circ$ : they are not equal unless both are $90^\circ$ .

c + e = 180^\circ

c and e: between the lines, same side, 60° + 120° = 180°