# Alternate Interior Angles

Author:
Erin

Two lines appear to be parallel and cut through by another line, CB, which we call a transversal. First, verify that these two lines are parallel using the slope tool. Then notice the marked angle FCD, this is called an interior angle because it falls between the two parallel lines. Angle ABF and angle FCD are referred to as alternate interior angles because they are on alternate sides of the transversal line. Predict what the relationship between angle FCD and ABF is.

Translate the circular arc of angle FCD along the vector CB. Add new points G and H where the arc intersects lines. What is true about FCD and angle GBH? Does this surprise you?

Rotate the circular arc GBH about the point B 180 degrees. What is the relationship between angle ABF and GBH?

What is the relationship between ABF and FCD? How do you know? (For example, how do these transformations "convince" you?)

Based on this exploration, make a conjecture about the supplementary alternate interior angles.