D and E are the points on the sides AB and AC respectively of a such that AD = 8 cm, DB = 12 cm, AE = 6 cm and CE = 9 cm. Prove that BC = 5/2 DE.

We have ,

= =

And, = =

Since,

Then , by converse of basic proportionality theorem.

DE||BC

In Δ ADE and Δ ABC

<A= <A (Common)

<ADE = <B (Corresponding angles)

Then, Δ ADE ~ Δ ABC (By AA similarity)

(Corresponding parts of similar triangle are proportion)

BC = 5/2 DE