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 / 要点
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 / 例题
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 / 记住
- Corresponding (F) and alternate (Z) angles are EQUAL.
- Co-interior (C) angles ADD to 180°.
- These rules only work when the lines are parallel.