Question

Based on the information given, can you determine that the quadrilateral must be a parallelogram? Explain. Given: XN NZ and NY = NW No; you cannot determine that the quadrilateral is a parallelogram. Yes; opposite sides are congruent. Yes; two opposite sides are both parallel and congruent. Yes; diagonals of a parallelogram bisect each other.

Answer 1

A parallelogram is a quadrilateral that has the following characteristics:

The opposite sides are parallel and congruent.

The opposite angles are congruent.

The consecutive angles are supplementary.

If any one of the angles is a right angle, then all the other angles will be at right angle.

The two diagonals bisect each other.

Since:

`XN\cong NZ;NY\cong NW`

We can conclude that the answer is:

Yes; diagonals of a parallelogram bisect each other. ​