When one line intersects two parallel lines diagonally, fixed relationships arise between the angles formed.
Relationships Between Angles of Parallel Lines
- Corresponding angles (angles in the same position): equal in measure (the shape of “F”)
- Alternate angles (angles on opposite sides): equal in measure (the shape of “Z”)
- Interior angles on the same side: their sum is 180° (the shape of “U” or “C”)
Example 1: Another line intersects two parallel lines. If one corresponding angle is 70°, what is the other angle?
Solution: Corresponding angles are equal, so the answer is 70°
Solution: Corresponding angles are equal, so the answer is 70°
Example 2: If one alternate angle is 55°, what is the other alternate angle? Also, what are the interior angles on the same side?
Solution:
① Alternate angles are equal, so the other one is also 55°
② Same-side interior angles sum to 180° → 180 − 55 = 125°
Solution:
① Alternate angles are equal, so the other one is also 55°
② Same-side interior angles sum to 180° → 180 − 55 = 125°
In geometry problems, it is often useful to draw an additional “parallel line (auxiliary line)” yourself and find corresponding or alternate angles. Try practicing this technique.