Question

In the given figure below, `(AD)/(AE) = (AC)/(BD)` and ∠1 = ∠2, Show that ΔBAE ∼ ΔCAD.

Answer 1

In ΔABC,

∠1 = ∠2

∴ AB = BD ......(i)

Given, `(AD)/(AE) = (AC)/(BD)`

Using equation (i), we get

`(AD)/(AE) = (AC)/(AB)`  ......(ii)

In ΔBAE and ΔCAD, by equation (ii),

`(AC)/(AB) = (AD)/(AE)`

∠A = ∠A  ......(Common)

∴ ΔBAE ∼ ΔCAD  ......[By SAS similarity criterion]