In the given figure below, AD/AE = AC/BD and ∠1 = ∠2. Show that ∆ BAE~ ∆CAD.

Solution:

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]