Question

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 1

l mujhe achcha laga ki main aapki madad ki

Answer 2

Hence Proved DE║BC

Step-by-step explanation:

Given:

$BA = AD$

$CA = AE$

We need to prove that segment DE║BC

Solution:

In Δ BAC and Δ DAE

$BA = AD$ ⇒ (Given)

$CA = AE$ ⇒ (Given)

$\angle BAC \cong \angle DAE$ ⇒ (Vertically opposite angles)

Hence we can say that;

By SAS congruence rule.

Δ BAC ≅ Δ DAE

So we can say that;

DE = BC

$\angle DEA = \angle BCA\\\\\angle EDA = \angle CBA$

By Congruence property.

Now we know that.

Two segments BC and DE are cut by a transversal  DB and also

$\angle EDA= \angle CBA$ ⇒ (Alternate angles)

Hence Proved DE║BC