In the given figure, if ∠ADE = ∠B, show that ΔADE ~ ΔABC. If AD = 3.8 cm, AE = 3.6 cm, BE= 2.1 cm and BC = 4.2 cm, find DE.

Given is that ∠ADE = ∠B

From the diagram clearly, ∠EAD = ∠BAC [∵ they are common angles]

Now, since two of the angles are correspondingly equal. Then by AA similarity criteria, we can say

∆ADE ∼ ∆ABC

Further, it’s given that

AD = 3.8 cm

AE = 3.6 cm

BE = 2.1 cm

BC = 4.2 cm

DE =?

To find AB, we can express it in the form AB = AE + BE = 3.6 + 2.1

⇒ AB = 5.7

So for the condition that ∆ADE ∼ ∆ABC,

Substituting given values in the above equation,

⇒

⇒

⇒ DE = 2.8

Thus, DE = 2.8 cm