In figure, the sides BA and CA have been produced such that BA = AD an

1.	In figure, the sides BA and CA have been produced such that BA = AD and CA = AE. Prove that segment DE ∥ BC.
Answer» Sides BA and CA have been produced such that BA = AD and CA = AE. To prove: DE ∥ BC Consider △BAC and △DAE, BA = AD and CA= AE (Given) ∠BAC = ∠DAE (vertically opposite angles) By SAS congruence criterion, we have △BAC ≃ △DAE We know, corresponding parts of congruent triangles are equal So, BC = DE and ∠DEA = ∠BCA, ∠EDA = ∠CBA Now, DE and BC are two lines intersected by a transversal DB s.t. ∠DEA=∠BCA (alternate angles are equal) Therefore, DE ∥ BC. Proved.

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

Answer»

Sides BA and CA have been produced such that BA = AD and CA = AE.

To prove: DE ∥ BC

Consider △BAC and △DAE,

BA = AD and CA= AE (Given)

∠BAC = ∠DAE (vertically opposite angles)

By SAS congruence criterion, we have

△BAC ≃ △DAE

We know, corresponding parts of congruent triangles are equal

So, BC = DE and ∠DEA = ∠BCA, ∠EDA = ∠CBA

Now, DE and BC are two lines intersected by a transversal DB s.t.

∠DEA=∠BCA (alternate angles are equal)

Therefore, DE ∥ BC. Proved.