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== == yes. suppose the quad ABCD has AB and CD equal and parallel. Then the triangles ABC and CDA are congruent by SAS axiom; so the quad is a parallelogram

Q: If one pair of sides of a quadrilateral is parallel and congruent then the quadrilateral is a parallelogram?

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The key is the object is quadrilateral with parallel sides. It is a parallelogram. It is also a rhombus.

A parallelogram has two pairs of congruent sides.

It is a rhombus or a parallelogram

No, it doesn't have to be. A quadrilateral can definitely be a parallelogram only if: - Both pairs of opposite sides are parallel. - Both pairs of opposite sides are congruent. - One pair of opposite sides are both congruent and parallel. - Both pairs of opposite angles are congruent. - The diagonals bisect each other.

diagonals.

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The key is the object is quadrilateral with parallel sides. It is a parallelogram. It is also a rhombus.

The Opposite Sides Parallel and Congruent Theorem states that if a quadrilateral has a pair of opposite sides that are parallel and congruent, then the quadrilateral is a parallelogram.

No. The congruent sides need not be parallel.

A parallelogram.

true

Parallel

Then, the opposite sides are congruent.

False

A parallelogram has two pairs of congruent sides.

parallelogram.

That's a parallelogram.

A parallelogram.