Q. 14.1( 38 Votes )

In Fig. 10.22, the sides BA and CA have been produced such that BA = AD and CA = AE. Prove that segment DE||BC.


Answer :

Given,

The sides BA and CA have been produced, such that:


BA = AD


And, CA = AE


We have to prove that,


DE BC


Consider and , we have


BA = AD and CA = AE (Given)


BAC = DAE (Vertically opposite angle)


So, by SAS congruence rule we have:



Therefore, BC = DE and


DEA = BCA,


EDA = CBA (By c.p.c.t)


Now, DE and BC are two lines intersected by a transversal DB such that,


DEA = BCA,


i.e., Alternate angles are equal


Therefore, DE BC


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