Section 5-2Ways to Prove

that Quadrilaterals

are Parallelograms

•If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

T S

RQ

Theorem 5-4

•If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.

T S

RQ

Theorem 5-5

•If both pairs of opposite angles of a quadrilateral congruent, then the quadrilateral is a parallelogram.

T S

RQ

Theorem 5-6

•If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

T S

RQ

Theorem 5-7

M

Five Ways to Prove that a Five Ways to Prove that a Quadrilateral is a ParallelogramQuadrilateral is a Parallelogram1. Show that both pairs of

opposite sides are parallel.2. Show that both pairs of

opposite sides are congruent.3. Show that one pair of opposite

sides are both congruent and parallel.

Five Ways to Prove that a Five Ways to Prove that a Quadrilateral is a ParallelogramQuadrilateral is a Parallelogram4. Show that both pairs of

opposite angles are congruent.

5. Show that the diagonals bisect each other.

Always, Sometimes or Never?

• The diagonals of a quadrialteral ___________ bisect each other.

• If the two measures of two angles of a quadrilateral are equal, then the quadrilateral is ____________ a parallelogram.

sometimes

sometimes

Always, Sometimes or Never?

• If one pair of opposite sides of a quadrilateral is congruent and parallel, then the quadrilateral is ____________ a parallelogram. always

Always, Sometimes or Never?

• If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is ____________ a parallelogram.

always

Always, Sometimes or Never?

• To prove a quadrilateral is a parallelogram, it is ____________ enough to show that one pair of opposite sides is parallel.

never