(Q20) In the given figure, ∠ADE = ∠B

i) Show that ∆ABC ∼ ∆ADE.

ii) If AD = 3.8 cm, AE = 3.6 cm, BE = 2.1 cm, BC = 4.2 cm, find DE.

Solution :

ABCED

i)Given :∆ABC and ∠ADE = ∠B

R.T.P : ∆ABC ∼ ∆ADE.

Proof : In ∆ABC and ∆ADE

∠A = ∠A [∵ Common]

∠B = ∠ADE [∵ Given]

∴ ∠C = ∠AED [∵ By Angle Sum property of triangles]

[∆ABC ∼ ∆ADE by AAA similarity condition.]

ii) AD = 3.8 cm, AE = 3.6 cm, BE = 2.1 cm, BC = 4.2 cm, find DE.

To find DE; ∆ABC ∼ ∆ADE

AB
AD
 =
BC
DE
 =
AC
AE

[∵ Ratios of corresponding sides are equal]

Thus
DE
 =
3.6 +
3.6
 =
3.6
   [∵ AB = AE + BE ]
⇒
DE
 =
⇒ DE =
×
=
∴ DE =
×
=
×
× 10
 =