Statements

Reasons 
1) E and F are mid points of AB and CD respectively 
1) Given 

2) AE = 1/2 AB and CF = 1/2 CD 
2) Definition of mid point 

3) ABCD is a parallelogram 
3) Given 

4)AB =CD and AB  CD 
4) Properties of parallelogram 

5) AE = FC and AE  FC 
5) From (2) and (4) 

6) AECF is a parallelogram 
6) Properties of parallelogram and from (5) 

7) FA  CE and FQ  CP 
7) Properties of Parallelogram 

8) F is the mid point of CD and FQ CP 
8) By Mid Point Theorem 

9) Q is the mid point of DP ⇒PQ = QD 
9) By Mid Point Theorem 

10)Similarly, P is the mid point of BQ ⇒ BP = PQ 
10) By mid point theorem

11) BP= PQ = QD 
11) From (9) and (10) 