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प्रश्न
In Δ ABC and Δ PQR,
∠ ABC ≅ ∠ PQR, seg BD and
seg QS are angle bisector.
`If (l(AD))/(l(PS)) = (l(DC))/(l(SR))`
Prove that : Δ ABC ∼ Δ PQR
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उत्तर
Proof : `(l(AD))/(l(PS)) = (l(DC))/(l(SR))` ∴ `(l(AD))/(l(DC)) = (l(PS))/(l(SR))`
According to angle bisector theorem, `(l(AD))/(l(DC)) = (l(AB))/(l(BC)) ; (l(PS))/(l(SR)) = (l(PQ))/((QR))`
`∴ (l(AB))/(l(BC)) = (l(PQ))/(l(QR))` and ∠ ABC ≅ ∠ PQR ..... (Given)
Δ ABC ∼ Δ PQR ........ (SAS Test)
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