Let `triangle ABC and triangle DEF` be two triangles given in such a way that AB||DE, AB = DE, BC||EF and BC = EF.
Prove that
(i) AC||DF and AC = DF,
(ii) `triangle ABC ~= triangle DEF.`

Explanation

AB||DE and AB = DE
`rArr ABED " is a ||gm " rArr " AD||BE and AD = BE. " ` …(i)
Again, BC ||EF and BC = EF
`rArr BEFC " is a ||gm "rArr " CF ||BE and CF = BE. " `…(ii)
From (i) and (ii), we get
AD|| CF and AD = CF.
`therefore ` ACFD is a ||gm.
Consequently, AC||DF and AC = DF.
`therefore triangle ABC ~= triangle DEF " " ` ( SSS-criterion).