PQR and SQR are two triangles on the same base QR If PS intersects QR at O then show - Maths -

Question

PQR and SQR are two triangles on the same base QR If PS
intersects QR at O then show that ar(PQR) divided by ar(SQR) = PO
divided by SO

Shridhar Kaushik · Accepted Answer

Draw PL⊥QR and SM⊥QR
In ∆PLO and ∆SMO,∠PLO = ∠SMO   90° each∠POL = ∠SOM  Vertically opposite angles⇒∆PLO ~  ∆SMO  AA similarity⇒PLSM = LOMO = POSO   Corresponding sides of similar ∆'s are proportional⇒PLSM = POSO   
1Now, ar ∆PQRar∆SQR = 12×QR×PL12×QR×SM⇒ar ∆PQRar∆SQR = PLSM⇒ar ∆PQRar∆SQR = POSO

PQR and SQR are two triangles on the same base QR. If PS intersects QR at O then show that ar(PQR) divided by ar(SQR) = PO divided by SO.