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Ways of Proving that a Quadrilateral is a Parallelogram

Parallelogram: A parallelogram is a quadrilateral whose opposite sides are parallel<br>Properties of a Parallelogram<br>1. Opposite sides of a parallelogram are congruent.<br>2. Opposite angles of a parallelogram are congruent.<br>3. Consecutive angles of a parallelogram are supplementary.<br>4. A diagonal of a parallelogram divides the parallelogram into two congruent triangles<br><br>If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram<br><br>If a quadrilateral's angle is supplementary to its adjacent angles, then the quadrilateral is a parallelogram.<br><br>

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Ways of Proving that a Quadrilateral is a Parallelogram

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  1. Ways of Provingthat Quadrilateralsare Parallelograms

  2. A parallelogram is a quadrilateral whose opposite sides are parallel. Parallelogram

  3. How do you knowthat a quadrilateralis a parallelogram?

  4. First, you must know whatthe properties of a parallelogram are.

  5. Properties of a Parallelogram Opposite sides of a parallelogram are congruent. B A D C

  6. Properties of a Parallelogram Opposite angles of a parallelogram are congruent. B A D C

  7. Properties of a Parallelogram Consecutive angles of a parallelogram are supplementary. B A m∠A + m∠B= 180o m∠B+ m∠C= 180o m∠C + m∠D= 180o m∠D+ m∠A= 180o C D

  8. Properties of a Parallelogram A diagonal of a parallelogram divides the parallelogram into two congruent triangles. B B A A C C D D

  9. From the converse of the previous theorems, here are the theorems that prove that a quadrilateral is a parallelogram.

  10. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. B A If AM ≅ CM BM ≅ DM M Then ABCD is a C D

  11. If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. B A If AB ≅DC AD ≅BC Then ABCD is a C D

  12. If an angle of a quadrilateral is supplementary to both its adjacent angles, then the quadrilateral is a parallelogram. B A If m∠A + m∠B= 180o m∠A + m∠D= 180o Then ABCD is a C D

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