CBSE
2026
Class Class 10 · Mathematics
3 Marks · Short
✅ Verified
S is a point on the side QR of a ΔPQR such that ∠PSR = ∠QPR. Prove that QR/RP = RP/RS.
✅ Answer & Solution
In ΔRPS and ΔRQP: $\angle PRS = \angle QRP$ (common angle at R). $\angle PSR = \angle QPR$ (given). By AA similarity, $\triangle RPS \sim \triangle RQP$. Therefore, $$\frac{RP}{RQ}=\frac{RS}{RP} \Rightarrow RP^2 = RQ\times RS \Rightarrow \frac{QR}{RP}=\frac{RP}{RS}$$ Hence proved.
✅ Verified by Super Admin
