Theorems Dealing with Parallelograms
Definition: A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
Properties
- 2 sets of parallel sides
- 2 sets of congruent sides
- opposite angles congruent
- consecutive angles supplementary
- diagonals bisect each other
- diagonals form 2 congruent triangles
Using this definition, the remaining properties regarding a parallelogram can be “proven” true and become theorems.
Proof of Theorem: If a quadrilateral is a parallelogram, the 2 pairs of opposite sides are congruent.
(Remember: when attempting to prove a theorem to be true, you cannot use the theorem as a reason in your proof.)
Proof of Theorem: If ONE PAIR of opposite sides of a quadrilateral are BOTH parallel and congruent, the quadrilateral is a parallelogram.
(Remember: when attempting to prove a theorem to be true, you cannot use the theorem as a reason in your proof.)
