Given:
ABCD is a parallelogram.
The objective is to prove AC and BD bisects each other.
Statement 1:
ABCD is a parallelogram.
Reason 1:
Given
Statement 2:
AB || CD.
Reason 2:
Definition of a parallelogram
Statment 3:
∠1 = ∠2 and ∠3 = ∠4.
Reason 3:
Alternate interior angle theorem.
Statement 4:
AB ≅ CD.
Reason 4:
Opposite sides of a parallelogram are congruent.
Statement 5:
△ABE≅△CDE
Reason 5:
ASA
Statement 6:
AE≅CE and BE≅DE.
Reason 6:
CPCTC
Statement 7:
AC and BD bisects each other at E.
Reason 7:
Definition of segment bisector.
Thus, the required reasons are provided for the given statements.