Based on the information given, can you determine that the quadrilateral must be a parallelogram? Explain.

Question

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

Answer 1

No, we cannot determine that the quadrilateral must be a parallelogram based on this information alone. While the congruent segments and intersection of the diagonals suggest that it could be a parallelogram, we would need additional information such as parallel sides or congruent opposite angles to prove that it is indeed a parallelogram.