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5.6 Proving That a Quadrilateral is a Parallelogram

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 . D. C. A. B.

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5.6 Proving That a Quadrilateral is a Parallelogram

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

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

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

  7. Given: NRTW is a parallelogram V W T X S Prove: XPSV is a parallelogram N P R 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

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