Question

In the figure, the sides BA and CA have been produced such that BA = AD and CA = AE. Prove the segment DE || BC.
NO SPAM ANSWERS......BEST ANSWER WILL BE AWARDED AS BRAINLIEST​

Answer 1

$\star\:\:\:\bf\large\underline\blue{Question:-}$

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

$\star\:\:\:\bf\large\underline\blue{Proof:-}$

In $\Delta ABC$ and $\Delta AED$,

$AB=AD$ (Given)

$AC=AE$ (Given)

$\angle DEA=\angle BAC$

Therefore, $\Delta ABC\cong \Delta AED (S.A.S)$

So,

$\angle EDB=\angle CBD$ (c.p.c.t)

But, they are alternate angle. Now, if alternate angles are equal, the lines are parallel.

So, $DE\parallel BC$

$\bf\large\underline\blue{Hence\:Proved.}$