Question

In the given figure, $\angle QPS=\angle RPTand\angle PRQ=\angle PTS$. [4 MARKS]
(i) Prove that $\Delta PQR\sim \Delta PST$
(ii) If PT:ST=3:4, find QR : PR.

Answer 1

Each part: 2 Marks

(i) Proof: $\angle QPS=\angle RPT$
Adding $\angle SPR$ on both sides, we get
$\Rightarrow \angle QPS+\angle SPR=\angle SPR+\angle RPT\Rightarrow \angle QPR+\angle SPTand\angle PRq=\angle PTs\left[Given\right]\therefore \Delta PQR\sim \Delta PST\left[AASimilarity\right]\left(ii\right)\frac{QR}{ST}=\frac{PR}{PT}[\Delta PQR\sim \Delta PST]\Rightarrow \frac{QR}{PR}=\frac{ST}{PT}=4:3$