Explore what happens when a line crosses a pair of parallel lines, and discover the special angle relationships that result.
When a line (called a transversal) crosses two parallel lines, it creates 8 angles. Corresponding angles (in matching positions) are equal, and alternate angles (on opposite sides of the transversal) are also equal.
A transversal crosses two parallel lines, forming a 65° corresponding angle pair. If one angle is 65°, what is its corresponding angle?
65°, since corresponding angles are equal
Two alternate interior angles are formed by a transversal. If one is 110°, what is the other?
110°, since alternate angles are equal
Co-interior angles (also called allied angles) lie on the same side of the transversal, between the two parallel lines. They always add up to 180°.
Two co-interior angles are formed between parallel lines by a transversal. If one is 70°, find the other.
180° − 70° = 110°
If two co-interior angles are equal, what must each one be?
90° each, since they must add to 180° and be equal
1. A transversal crosses two parallel lines. One corresponding angle is 55°. Find its matching corresponding angle.
2. Two alternate interior angles are formed. If one is 95°, find the other.
3. Two co-interior angles are formed between parallel lines. If one is 120°, find the other.
4. A transversal crosses two parallel lines, forming an angle of 40° with one line. What is the co-interior angle on the same side?
5. If two lines are NOT parallel, do corresponding angles formed by a transversal have to be equal?