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6.3 Proving Quadrilaterals are Parallelograms

6.3 Proving Quadrilaterals are Parallelograms. Objective: To learn how to prove quadrilaterals are parallelograms. A. B. D. C. theorem. 1. If a quadrilateral has both pairs of opposite sides congruent,. then it is a parallelogram. parallelogram. A. B. D. C. theorem.

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6.3 Proving Quadrilaterals are Parallelograms

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  1. 6.3 Proving Quadrilaterals are Parallelograms Objective: To learn how to prove quadrilaterals are parallelograms

  2. A B D C theorem 1. If a quadrilateral has both pairs of opposite sides congruent, then it is a parallelogram parallelogram

  3. A B D C theorem 2. If a quadrilateral has both pairs of opposite angles congruent, then it is parallelogram. parallelogram

  4. A B D C theorem 3. If a quadrilateral hasone angle that is supplementary to both of its consecutive angles, then it is a parallelogram. parallelogram

  5. A B D C theorem 4. If a quadrilateral’s diagonals bisect each other, then it is a parallelogram parallelogram M

  6. A B D C theorem 5.If a quadrilateralhasone pair of opposite sides parallel and congruent, then it is a parallelogram parallelogram

  7. Example Decide whether you are given enough information to determine that the quadrilateral is a parallelogram. Explain your reasoning. YES One angle is supplementary to both of its consecutive angles

  8. Example Decide whether you are given enough information to determine that the quadrilateral is a parallelogram. Explain your reasoning. YES Opposite angles of a quadrilateral are congruent.

  9. Example Decide whether you are given enough information to determine that the quadrilateral is a parallelogram. Explain your reasoning. YES Definition of a parallelogram

  10. Example Describe how you would prove that ABCD is a parallelogram. Congruent alternate interior angles make parallel lines. One pair of opposite sides are parallel and congruent.

  11. Example Describe how you would prove that ABCD is a parallelogram. Congruent alternate interior angles make parallel lines. Definition of parallelogram

  12. Example Describe how you would prove that ABCD is a parallelogram. Congruent alternate interior angles make parallel lines. Congruent corresponding angles make parallel lines. Definition of parallelogram

  13. P Q T R S Statement Reason

  14. P Q T R S Statement Reason

  15. start w/ parallelogram Get opposite sides || Get opposite sides Get opposite angles Get supplementary consecutive angles Get diagonals that bisect each other To get a parallelogram Show opposite sides || Show opposite sides Show opposite angles Show consecutive angles are supplementary Show diagonals bisect each other Show one pair of opposite sides are both || and Summary

  16. y Show opposite sides x Show that quadrilateral ABCDis a parallelogram Show opposite sides || ( – 1, 2) A ( 3, 2) B 1 1 –4 C (1, – 2) D ( – 3, – 2) –3

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