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Theorem 2 - In a Parallelogram Opposite Sides are Equal

Given: A ïïgm ABCD
To Prove: AB = DC and AD = BC
Construction: Join A to C.

Proof :
AB
ïï DC with transversal AC
...    
1 = 4 ......(Alternate interior angles of parallel sides)
Similarly      
2 = 3
Now in
Δ ABC and Δ ADC, we have
       
 ∠1 = 4, 2 = 3
and   AC = AC (Common)
...    
ΔABC ΔACD
...     AB = DC            (CPCT)
and AD = BC       ...... (CPCT)





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