5 6 Proving That a Quadrilateral is a
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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.
Methods to prove quadrilateral ABCD is a parallelogram A D C B 1. If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram (reverse of the definition). 2. If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram (converse of a property).
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).
F E D Given: ACDF is a parallelogram Prove: FBCE is a parallelogram A 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. B C
A Given: Prove: BARK is a parallelogram 1. 2. 3. 4. 5. 6. 7. 8. 9. C B R K
Q D Given: Quadrilateral QUAD with angles as shown Show that QUAD is a parallelogram A U
Given: NRTW is a parallelogram V W T X S Prove: XPSV is a parallelogram N 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. P R
Summary Using one of the methods to prove quadrilaterals are parallelograms, create your own problem and show it is a parallelogram. Homework: worksheet
