In the given figure the sides BA and CA have been produced such that BA=AD and CA=AE.Prove that the segment DE||side BC
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the sides BA and CA have been produced such that BA= AD and CA=AE and given to prove DE|| BC
Consider triangle BAC and DAE,
We have BA = ADand CA = AE [∴ given in the data] And also ∠BAC =∠DAE [∴ vertically opposite angles] So, by SAS congruence criterion,
we have ΔBAC ≅ ΔDAE ⇒ BC = DE and ∠DEA=∠BCA,∠EDA=∠CBA [Corresponding parts of congruent triangles are equal]
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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