Question

If AD = AE and BD = CE then ______.

Options

• △ ADE ∼ △ ACB

• △ ABC ∼ △ ACB

• △ ABD ∼ △ ABC

• △ ADE ∼ △ ABC

Answer 1

If AD = AE and BD = CE then △ ADE ∼ △ ABC.

Explanation:

Given,

⇒ AD = AE = x (let)

⇒ BD = CE = y (let)

From figure,

⇒ AB = AD + BD = x + y

⇒ AC = AE + EC = x + y

In △ ADE and △ ABC,

⇒ ∠DAE = ∠BAC

⇒ `(AD)/(AB) = (AE)/(AC) = x/(x+y)`

∴ △ ADE ~ △ ABC (By S.A.S. postulate)