Unit 1, Lesson 9

Transformations, Transversals, and Proof

Integrated Math 2

Practice

1. Problem 1

   Student Task Statement

   Priya: “I bet if the alternate interior angles are congruent, then the lines will have to be parallel.”

   Han: “Really? We know if the lines are parallel then the alternate interior angles are congruent, but I didn't know that it works both ways.”

   Priya: “Well, I think so. What if angle  and angle are both 40 degrees? If I draw a line perpendicular to line through point , I get this triangle. Angle would be 50 degrees because . And because the angles of a triangle sum to 180 degrees, angle is 90 degrees. It's also a right angle!”

   Han: “Oh! Then line and line are both perpendicular to the same line. That's how we constructed parallel lines, by making them both perpendicular to the same line. So lines and must be parallel.”

   

   Horizontal lines A I and G J. Line F E passes through line G J at point C and line A I at point B. 

   1. Label the diagram based on Priya and Han's conversation.
   2. Is there something special about 40 degrees? Write a conjecture about a pair of alternate interior angles measuring degrees.
   3. Prove your conjecture.