1. Your teacher will give you a set of cards that show different figures. Sort the cards into categories of your choosing. Be prepared to explain the meaning of your categories.

2. Sort the cards by rigid vs. flexible figures. 

3. State at least one set of triangles that can be proved congruent using the:

   1. Side-Angle-Side Triangle Congruence Theorem.

   2. Angle-Side-Angle Triangle Congruence Theorem.

   3. Side-Side-Side Triangle Congruence Theorem.

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.