Question

In the given figure, ∠D = ∠E and `"AD"/"DB" = "AE"/"EC"` Prove that ΔABC is isosceles.

Answer 1

Given:

∠D = ∠E

`"AD"/"BD" = "AE"/"EC"`

To Prove: ΔABC is isosceles

Proof: In ΔADE

∠D = ∠E

And, `"AD"/"BD" = "AE"/"EC"`   ...(given)

∴ `"DE"/"BC"`   ...(By converse of B.P.T)

In ΔABC

∠D = ∠B   ...[Corresponding's are equal]

∠E = ∠C

Thus ∠B = ∠C   ...(from (i))

∴ AB = AC (sides opposite to equal angles) are equal Hence, ΔABC is isosceles.