Answer:
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 parallelogramTriangles can be similar or congruent. Similar triangles will have congruent angles but sides of different lengths. Congruent triangles will have completely matching angles and sides. Their interior angles and sides will be congruent. Testing to see if triangles are congruent involves three postulates, abbreviated SAS, ASA, and SSS.