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

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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]

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