Question

1.If a quadrilateral is a parallelogram, then the diagonals bisect each other. help not sure if I did this right

this is what I have so far
1. ZKUH is the parallelogram and the diagonals (ZU) ̅ and (KH) ̅ intersect at point E its given
2.< HKZ ≅ < UHK & < KZU ≅ < ZUH &
< UKH ≅ < KHZ & < UZH ≅ < KUZ 2by the converse of the alternate interior angles theorem
3.triangle KUH ≅ triangle KZH by the ASA theorem [KH = KH by step 2.]
4.KZ ≅ HU & KU ≅ HZ by CPCTC
5.triangle KEZ ≅ triangle HEUby the ASA theorem [steps 2. & 4.]
6.ZE ≅ EU & KE ≅ EH by CPCTC

Answer 1

For step two should it be by the converse of the alternate interior angles theorem
or just by alternate interior angles theorem ?

Answer 2

Given: Quadrilateral ZKUH is a parallelogram
Prove: The diagonals of parallelogram bisect each other