Take turns with your partner to match a statement with a diagram that could go with that proof. For each match you find, explain to your partner how you know it’s a match. For each match your partner finds, listen carefully to their explanation. If you disagree, discuss your thinking, and work to reach an agreement.

1. A quadrilateral with perpendicular diagonals that bisect each other is equilateral.
2. If one diagonal of a quadrilateral is the perpendicular bisector of the other, then 2 pairs of adjacent sides are congruent.
3. Opposite angles in an equilateral quadrilateral are congruent.
4. In a parallelogram, opposite sides are congruent.

1. Watch the video, and record the steps to cut the wooden planks to fit around the beam.
2. Test your steps with your partner.
   • Partner A: Cut 2 pieces of tracing paper to represent the wooden planks. Follow the instructions your partner gives you.
   • Partner B: Read your steps aloud. Adjust your instructions if necessary until the method works.

   

3. Label the diagram and tracing paper so that you can rewrite the conjecture more precisely: “Following these steps will always create 2 pieces that fit together exactly.”
4. Write a proof for your precise conjecture.