Question

Given: △KOE∼△LSV, OT and SP are angle bisectors Prove: OT/TE = SP/PV

Answer 1

Explanation:

Given: △KOE∼△LSV, OT and SP are angle bisectors that is ∠KOT=∠TOE and ∠LSP=∠PSV.

To Prove:
`(OT)/(TE)=(SP)/(PV)`

Proof: Since, OT and SP are angle bisectors that is ∠KOT=∠TOE and ∠LSP=∠PSV, and ∠KOE=∠LSV (given).Therefore, ∠TOE=∠PSV (1)

Consider △OTE and △PSV,

∠E = ∠V (△KOE∼△LSV)

∠TOE=∠PSV(From (1)

Thus, by AA similarity, △OTE is similar to △PSV, therefore using similarity condition,

`(OT)/(TE)=(SP)/(PV)`

Hence proved.