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
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