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Chapter 6: Quadrilaterals

Chapter 6: Quadrilaterals. 6.3 Proving That a Quadrilateral is a Parallelogram. theorems. Th. 6-5 If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Th. 6-6

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Chapter 6: Quadrilaterals

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  1. Chapter 6: Quadrilaterals 6.3 Proving That a Quadrilateral is a Parallelogram

  2. theorems • Th. 6-5 • If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. • Th. 6-6 • If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

  3. theorems • Th. 6-7 • If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. • Th. 6-8 • If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.

  4. Example 1 • For what value of x must MLPN be a parallelogram?

  5. Example 1a • Find the values of a and c for which PQRS must be a parallelogram.

  6. Example 2 • Can you prove this? • Given: • Prove: ABCD is a parallelogram

  7. Example 2a • Can you prove this? • Given: • Prove: LMNO is a parallelogram

  8. Example 3 • Find the values for x and y that make ABCD a parallelogram:

  9. Example 3a • Find the measures of the numbered angles:

  10. Homework

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