Geometry Notes, March 19th

Theorems, Postulates, and Definitions.


Theorem 8-8: If two pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Theorem 8-10: If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Theorem 8-11: If the diagonals of a quadrilateral bisect each other then the quadrilateral is a parallelogram.


Theorem 8-12: If one pair of opposite sides of a quadrilateral are parellel and congruent, then the quadrilateral is a parrelellagram.

Summary!

A quadrilateral is a parallelogram if any one of the following statements are true.
1. Both pairrs of opposite sides are parrallel. (definition)
2. Both pairs of opposite sides are congruent. (theorem 8-9)
3. Both pairs of opposite angles are congruent (throrem -10)
4. The diagnols bisect each other (theorem 8-11)
5. A pair of opposite sides is both parellel and congruent (theorem 8-12)

Parallelograms in the coordinate plane

• The slope formula can be used to determine if the opposite sides have the same slope.
• The distance formula can be used to see if the opposite sides are congruent or
• The slope and the distance formula ccan be used to determine if one pair of opposite sides is parallel and congruent.