Question

If the angle bisectors of a pair of opposite angles of a quadrilateral are the opposite sides of a parallelogram formed by the two angle bisectors and two sides of the quadrilateral, is the quadrilateral always a parallelogram? Explain your answer.

Answer 1

Yes

Explanation:

I do rsm

Answer 2

The correct answer is;

No, the quadrilateral is not always a parallelogram

Explanation:

Since there are only four opposite angles in a quadrilateral there are only two possible angle bisectors of the opposite angles also, the angle bisectors of a pair of opposite angles of a quadrilateral will intersect within the quadrilateral and therefore they cannot form the sides of a parallelogram

Therefore, the answer is no, the quadrilateral is not always a parallelogram.