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In the given figure, BA|AC and DE|DF suc...

In the given figure, `BA_|_AC and DE_|_DF` such that AB = DE and BF = EC. Show that `DeltaABC~=DeltaDEF.`

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GIVEN `BA_|_AC and DE_|_DF` such that `aB=DE and BF=EC.`
TO PROVE `DeltaABC~=DeltaDEF.`
PROOF `" "EC=BF rArr BE-EC=BE-BF`
`rArr BC=EF." …(i)"`
In `DeltaABC and DeltaDEF`, we have
`AB=DE" (given)"`
`angleBAC=angleEDF=90^(@)`
`"hyp. BC = hyp. EF"`
`therefore" "DeltaABC~=DeltaDEF" [by RHS-criteria]."`
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