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Based on the information given, can you determine that the quadrilateral must be a parallelogram? Explain.
Given: Segment X N is congruent to segment N Zand Segment N Y is congruent to segment N W
the figure is quadrilateral W X Y Z with diagonals X Z and W Y that meet at point N
Yes, based on the given information, we can determine that the quadrilateral WXYZ must be a parallelogram.
By definition, a parallelogram is a quadrilateral with two pairs of opposite sides that are congruent and parallel.
In this case, we are given that segment XN is congruent to segment NZ, and segment NY is congruent to segment NW. This means that opposite sides XZ and WY are congruent.
Additionally, the diagonals XZ and WY meet at point N. In a parallelogram, the diagonals bisect each other, meaning that they divide each other into two equal segments. Since segment XN is congruent to segment NZ, and segment NY is congruent to segment NW, it follows that the diagonals XZ and WY bisect each other at point N.
Therefore, based on the given information, we can conclude that the quadrilateral WXYZ must be a parallelogram.