5-3: PROVING PARALLELOGRAMS Mr. Schaab’s Geometry Class Our Lady of Providence Jr.-Sr. High School

Proving Parallelograms  Now that we know all the features of a parallelogram, when we’re given a parallelogram we can tell a lot about it. But what if we’re given a quadrilateral and we’re trying to PROVE that it is a parallelogram?  We need to work backwards and use the properties we know about parallelograms to help us prove it.

Theorem Converses  Definition of a Parallelogram:  If a quadrilateral is a parallelogram, then both pairs of opposite sides are parallel.  Converse of the definition of a Parallelogram:  If both pairs of a quadrilateral’s opposite sides are parallel, then it is a parallelogram.

Theorem Converses  Theorem 5.3:  If a quadrilateral is a parallelogram, then its opposite sides are congruent.  Converse of Theorem 5.3:  If a quadrilateral’s opposite sides are congruent, then it is a parallelogram.

Theorem Converses  Theorem 5.4:  If a quadrilateral is a parallelogram, then its opposite angles are congruent.  Converse of Theorem 5.4:  If a quadrilateral’s opposite angles are congruent, then it is a parallelogram.

Theorem Converses  Theorem 5.6:  If a quadrilateral is a parallelogram, then its diagonals bisect each other.  Converse of Theorem 5.6:  If a quadrilateral’s diagonals bisect each other, then it is a parallelogram.

One More Theorem… Reflexive Property Alternate Interior Angles Thm. SAS Given CPCTC Alternate Interior Angles Converse Definition of Parallelogram Converse

One Pair of Parallel and Congruent Sides  Theorem 5.7 – If a quadrilateral has one pair of sides that are parallel AND congruent, then it is a parallelogram.  Mark it!

Homework  There will be a HW Quiz over Unit 5-3 on Wednesday, Dec. 9! (Thursday for Geo. 2B)  5-3 HW: Complete Prac. #1-7 ALL, Apps. #1-3 ALL  Remember: You may use your homework to help you with the HW Quiz, so write down each problem on paper!