Given: in quadrilateral wxyz , and bisect each other at point a. prove: quadrilateral wxyz is a parallelogram. statement reason 1. and bisect each other. given 2. wa = ya xa = za definition of bisection 3. m∠yaz = m∠xaw vertical angles theorem 4. sas criterion for congruence 5. ∠ ywx ≅ ∠wyz corresponding angles of congruent triangles are congruent. 6. || converse of alternate interior angles theorem 7. m∠xay = m∠zaw vertical angles theorem 8. ∆xay ≅ ∆zaw sas criterion for congruence 9. ∠xzw ≅ ∠zxy corresponding angles of congruent triangles are congruent. 10. || converse of alternate interior angles theorem 11. quadrilateral wxyz is a parallelogram. definition of parallelogram what is the missing statement in this proof? what is the missing statement in this proof?

Step-by-step explanation:

Given:In quadrilateral WXYZ , and diagonals bisect each other at point A.

To prove: Quadrilateral WXYZ is a parallelogram.

Proof: Reason 1. Diagonals bisect each other (given)

2.WA=YA and XA=ZA by the definition of bisection.

3. m∠YAZ = m∠XAW Vertical Angles theorem.

4. By the SAS criterion for congruence, ΔWAX≅ΔZAY.

5.∠ YWX ≅ ∠WYZ (Corresponding angles of congruent triangles are congruent).

6.. || converse of Alternate Interior Angles Theorem .

7. m∠XAY = m∠ZAW Vertical Angles Theorem and XA=ZA and WA=YA by the definition of bisection.

8.∆XAY ≅ ∆ZAW SAS criterion for congruence.

9.∠XZW ≅ ∠ZXY Corresponding angles of congruent triangles are congruent.

10.|| converse of Alternate Interior Angles Theorem.

11. Quadrilateral WXYZ is a parallelogram by the definition of parallelogram.

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step-by-step explanation: