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Proving That a Quadrilateral is a Parallelogram

Proving That a Quadrilateral is a Parallelogram. Chapter 6 Section 3. Objective. Students will determine whether a quadrilateral is a parallelogram. Parallelogram. You can decide whether a quadrilateral is a parallelogram if its sides, angles, and diagonals have certain properties.

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Proving That a Quadrilateral is a Parallelogram

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  1. Proving That a Quadrilateral is a Parallelogram Chapter 6 Section 3

  2. Objective • Students will determine whether a quadrilateral is a parallelogram.

  3. Parallelogram • You can decide whether a quadrilateral is a parallelogram if its sides, angles, and diagonals have certain properties

  4. Theorem 6-8 • If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

  5. Theorem 6-9 • If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram.

  6. Theorem 6-10 • If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

  7. On page 368… • Look at Problem 1

  8. Theorem 6-11 • If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

  9. Theorem 6-12 • If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.

  10. On page 370… • Look at Problem 2.

  11. Proving That a Quadrilateral is a Parallelogram • Prove that both pairs of opposite sides are parallel • Prove that both pairs 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 congruent and parallel.

  12. On page 372… • Try problems #1-6 on your own.

  13. Beginning on page 372… • Complete problems #7-28.

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