6.2 Properties of parallelograms

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6-2 Properties of Parallelograms

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Presentation transcript:

6.2 Properties of parallelograms

Parallelogram A quadrilateral with both pairs of opposite sides parallel. We will use this symbol to shorten things up… The following are several theorems that are true for all parallelograms, they can be proven (which we will do) by using what we have learned about parallel lines and congruent triangles.

Theorem Opposite sides of a parallelogram are congruent.

proof Given: EFGH Prove:

Theorem Opposite angles of a parallelogram are congruent

Theorem Diagonals of a parallelogram bisect each other

Proof Given: QRST with diagonals QS and TR 1 3 Given: QRST with diagonals QS and TR Prove: QS and TR bisect each other 4 2

Theorem Consecutive angles in a parallelogram are supplementary. -Think about why?