This investigation is about discovering the relationships sides, angles, and the diagonals of the parallelogram. Try to discover which lengths are congruent, parallel, perpendicular, or bisected. Discover which angles are congruent, complementary, supplementary, or bisected. Try to generalize your findings by using descriptions like opposite or consecutive with what and how many that applies to. For example a generalization might be: “One pair of opposite sides are parallel.” On the polygon put markings of congruency, right angles, or parallel for the sides or angles.

1. Are any of the sides parallel? Which pairs?
2. Are any of the sides perpendicular? Which pairs?
3. Are any of the sides congruent? Which pairs?
4. Are any of the angles congruent? Which pairs?
5. Are any of the angles supplementary? Which pairs?
6. Are the diagonals congruent?
7. Do the diagonals bisect each other?
8. Do the diagonals bisect opposite angles?
9. Are the diagonals perpendicular?