Parallel lines and a transversal
Parallel lines never meet and stay the same distance apart. A transversal is a line that crosses two (or more) parallel lines. This creates special pairs of equal angles.
The three angle rules
Key idea
Corresponding angles are equal (they sit in matching positions, like an F shape). Alternate angles are equal (they sit inside, on opposite sides, like a Z shape). Interior angles on the same side add up to 180° (like a C shape).
- Corresponding angles: same corner at each crossing — equal.
- Alternate angles: between the parallel lines, opposite sides of the transversal — equal.
- Co-interior (allied) angles: between the parallel lines, same side — add to 180°.
Using the rules
Worked example
A transversal cuts two parallel lines. One angle is 116°. Find the corresponding angle, the co-interior angle and an alternate angle.
Corresponding angle = 116° (equal).
Co-interior angle = 180° − 116° = 64°.
Alternate angle to that 64° angle = 64°.
Check: the two co-interior angles 116° + 64° = 180°. Correct.
Remember
- Corresponding (F) and alternate (Z) angles are EQUAL.
- Co-interior (C) angles ADD to 180°.
- These rules only work when the lines are parallel.