1. 5.6 Proving That a Quadrilateral is a Parallelogram Objective: After studying this section, you will be able to prove that a quadrilateral is a parallelogram.

2. Methods to prove quadrilateral ABCD is a parallelogram 1. If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram (reverse of the definition). A B DC 2. If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram (converse of a property).

3. 3. If one pair of opposite sides of a quadrilateral are both parallel and congruent, then the quadrilateral is a parallelogram. 4. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram (converse of a property). 5. If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram (converse of a property).

4. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Given: ACDF is a parallelogram Prove: FBCE is a parallelogram C E A D F B 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

5. 1. 2. 3. 4. 5. 6. 7. 8. 9. Given: CK A R B 1. 2. 3. 4. 5. 6. 7. 8. 9. Prove: BARK is a parallelogram

6. Given: Quadrilateral QUAD with angles as shown Show that QUAD is a parallelogram U A Q D

7. Given: NRTW is a parallelogram Prove: XPSV is a parallelogram R T N W V S P X 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

8. Summary Using one of the methods to prove quadrilaterals are parallelograms, create your own problem and show how it is a parallelogram. Homework: worksheet