Question

The sides BA and CA have been produced such that BA =AD & CA = AE .Prove that DE || BC.

Answer 1

Answer:

in triangle ABC and triangle ADE

angle BAC=angle DAE

AC=AE

AB=AD

by sas test

the triangles are congruent

by CPCT

angle DEC=angle BCA

but those two are alternate angles

thus by alternate angle test

DE||BC

Answer 2

Answer:

Step-by-step explanation:

Solution:

Given : Sides BA and CA of ∆ABC are produced such that BA = AD are CA = AE. ED is joined.

To prove : DE || BC

Proof: In ∆ABC and ∆DAE AB=AD (Given)

AC = AE (Given)

∠BAC = ∠DAE (Vertically opposite angles)

∴ ∆ABC ≅ ∆DAE (SAS axiom)

∴ ∠ABC = ∠ADE (c.p.c.t.)

But there are alternate angles

∴ DE || BC