Question

In the fig 12.22, the sides BA and CA have been produced such that BA =AD and CA =AE. Prove that segment DE|| BC​

Answer 1

Answer:

in triangles ABC and ADE,

BA =AD(given)

CA =AE.(given)

Angle BAC = Angle DAE

Therefore, triangles ABC and ADE are congruent.

So, angle ABC = angle ADE

they are alt. int. angles

So, 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