Question

Select the correct answer. Given: In quadrilateral WXYZ, the diagonals WX and YZ bisect each other at point A. Prove: Quadrilateral WXYZ is a parallelogram. Which statement is missing in this proof?

1) ΔXAW ≅ ΔYAZ
2) ΔXAY ≅ ΔZAW
3) WY = XZ
4) ΔXZW ≅ ΔZXY

Answer 1

To prove that quadrilateral WXYZ is a parallelogram, we can use the given information that the diagonals WX and YZ bisect each other at point A. From this, we can show that triangle XAW is congruent to triangle YAZ, and therefore opposite sides WY and XZ are congruent.

Step-by-step explanation:

In order to prove that quadrilateral WXYZ is a parallelogram, we need to show that opposite sides are parallel and congruent. From the given information, we know that the diagonals WX and YZ bisect each other at point A. This means that triangle XAW is congruent to triangle YAZ (using the Side-Side-Side congruence theorem). Since corresponding parts of congruent triangles are congruent, we can conclude that opposite sides WY and XZ are congruent, which proves that quadrilateral WXYZ is a parallelogram.