Step-by-step explanation:
Since we have given that
Given: △KOE∼△LSV,
OT and SP are angle bisectors.
To Prove: OT/TE = SP/PV
Proof: Consider △OTE and △PSV,
∠E = ∠V (∵ △KOE∼△LSV)
∠KOE = ∠LSV
[tex]\frac{1}{2}\angle KOE=\frac{1}{2}\angle LSV\\\\\angle TOE=\angle PSV[/tex]
( ∵ OT and PS are the angle bisectors)
OE = SV (∵ △KOE∼△LSV)
By SAS criteria, △OTE ≈ △PSV
So, ratio will be
[tex]\frac{OT}{TE}=\frac{SP}{PV}[/tex]
Hence, Proved.
