Question

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?

Answer 1

Answer:

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.

Answer 2

Answer:

its B

Step-by-step explanation:

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