When one line intersects two lines, corresponding angles (angles in the same position on the same side) and alternate angles (angles in crossed positions) are formed. When the two lines are parallel, corresponding angles are equal, and alternate angles are also equal.
Example ①
Two lines are parallel, and an angle formed with the transversal is 70°. Find the corresponding angle and the alternate angle.
Answer: Corresponding angle = 70° (equal when the lines are parallel). Alternate angle = 70° (equal when the lines are parallel).
Two lines are parallel, and an angle formed with the transversal is 70°. Find the corresponding angle and the alternate angle.
Answer: Corresponding angle = 70° (equal when the lines are parallel). Alternate angle = 70° (equal when the lines are parallel).
Example ② (Finding an Angle)
l ∥ m, and one angle is 55°. Find angle x using corresponding angles. (x is an angle in the position of an alternate angle.)
Answer: Since alternate angles are equal, x = 55°
l ∥ m, and one angle is 55°. Find angle x using corresponding angles. (x is an angle in the position of an alternate angle.)
Answer: Since alternate angles are equal, x = 55°
Key Points
- Parallel lines ⇒ corresponding angles are equal, and alternate angles are equal (the converse also holds)
- Corresponding angles: F-shaped angles
- Alternate angles: Z-shaped angles
Practice Problem
- When l ∥ m, give the corresponding angle and the alternate angle of ∠x = 130°.
Answer and Explanation
- Answer: Corresponding angle 130°, alternate angle 130°.