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6-3

6-3. Proving Parallelograms. OBJECTIVE. To determine whether a quadrilateral is a parallelogram. KEY CONCEPT. To prove a quadrilateral is a parallelogram:. KEY CONCEPT. To prove a quadrilateral is a parallelogram:. KEY CONCEPT. To prove a quadrilateral is a parallelogram:. 1.

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6-3

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  1. 6-3 Proving Parallelograms

  2. OBJECTIVE To determine whether a quadrilateral is a parallelogram

  3. KEY CONCEPT To prove a quadrilateral is a parallelogram:

  4. KEY CONCEPT To prove a quadrilateral is a parallelogram:

  5. KEY CONCEPT To prove a quadrilateral is a parallelogram: 1 m 1 + m 2 = 180 m 2 + m 3 = 180 2 3

  6. KEY CONCEPT To prove a quadrilateral is a parallelogram:

  7. KEY CONCEPT To prove a quadrilateral is a parallelogram:

  8. KEY CONCEPT To prove a quadrilateral is a parallelogram:

  9. CLASS WORK Can you prove that the quadrilateral is a parallelogram based on the given information? Explain. 1. 2. 3. 4.

  10. CLASS WORK For what values of x and y must the figure be a parallelogram? 5. 6.

  11. CLASS WORK For what values of x and y must the figure be a parallelogram? 7. 8.

  12. EXIT PROBLEMS For what values of x and y must the figure be a parallelogram? 9. 10.

  13. SUMMARY A quadrilateral is a parallelogram if: Prove that both sets of opposite sides are parallel. Prove that both sets of opposite sides are congruent. Prove that an angle is supplementary to both of its consecutive angles. Prove that both pairs of opposite angles are congruent. Prove that the diagonals bisect each other. Prove that one pair of opposite sides is parallel and congruent.

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