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Converse of Theorem 2

"If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram."

 

Given: A quadrilateral ABCD, in which AB = DC and AD = BC.
To Prove: Quadrilateral ABCD is a parallelogram.
Construction: Join AC.


Proof:
In
Δ ABC and Δ ADC,
AB = DC, AD = BC...... (given)
and         AC = AC...... (common)
...      
Δ ABC Δ ADC..... (sss. criterian)
...         
1 = 2...... (CPCT)
and       
3 = 4 ..... (CPCT)
Therefore AB
ïï DC and AD ïï BC
Quadrilateral ABCD is a parallelogram.





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