In the given figure below, AD/AE = AC/BD and ∠1=∠2.. Show that Δ BAE~ΔCAD .
In ∆ABC, ∠1=∠2
∴ AB = BD ..............(i)
Given, ADAE=ACBD
Using equation (i), we get ADAE=ACAB .............(ii)
In ΔBAE and ΔCAD, by equation (ii), ACAB=ADAE
and ∠A=∠A (common)
∴ ΔBAE ~ ΔCAD [By SAS similarity criterion]