Question

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

Answer 1

From given figure,

∠ADE = ∠B

To prove:

∆ADE ~ ∆ABC and

find DE

Given: AD = 3.8 cm, AE = 3.6 cm, BE = 2.1 cm and BC = 4.2 cm

Now, In ∆ADE and ∆ABC

∠ADE = ∠B (given)

∠A = ∠A (common)

∆ADE ~ ∆ABC (By AA)

Again,

AD/AB = DE/BC