(Q12) Explain why the triangles are similar and then find the value of x.

iii)

ABCEDx222414

Solution :

Given : In △ABC and △ECD

∠A = ∠E

∠ACB = ∠ECD [∵ Vertically opposite]

∴ ∠B = ∠D [∵ angle sum property]

∴ △ABC ~ △EDC

⇒
AB
ED
 =
BC
DC
 =
AC
EC
⇒
=
x
 ⇒ x =
×
=