Q: What quadrilateral is two pair of opposite angle congruent?

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A kite

No, you need both pairs of opposite sides to be congruent (i.e. the same size) to be a parallelogram.

Kite

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.

Related questions

For the quadrilateral to be a parallelogram, both pairs of opposite angles must be congruent.

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.

Then, the opposite sides are congruent.

sometimes

Parallel

draw a diagonal through opposite corners of the quadrilateral. This makes two triangles. Prove the triangles are congruent using SSA (side side angle) congruence. Then show that the other two sides of the quadrilater must be congruent to each other, so it is a parallelogram.

How about a trapezoid as an example.

No, it is not.

A kite

This quadrilateral is a trapezoid. In a trapezoid, one pair of opposite sides is parallel, and one pair of opposite sides is congruent. The other two sides are not parallel or congruent.

No, you need both pairs of opposite sides to be congruent (i.e. the same size) to be a parallelogram.