Question

In the adjoining figure, if QR = SR and ∠PRQ = ∠PRS then show that
a) PQ=PS
b) ∆PRQ ≅ ∆PRS ​

Answer 1

Step-by-step explanation:

Answer

Given that:

QP=8cm,PR=6cm and SR=3cm

(I)  In △PQR and △SPR

∠PRQ=∠SRP  (Common angle)

∠QPR=∠PSR   (Given that)

∠PQR=∠PSR   (Properties of triangle )

∴△PQR∼△SPR  (By AAA)

(II)   SPPQ=PRQR=SRPR  (Properties of similar triangles)

⇒SP8cm=3cm6cm

⇒SP=4cm and 

⇒6cmQR=3cm6cm

⇒QR=12cm

(III)ar(△SPR)ar(△PQR)=SP2PQ2=4282=4

mark as brainlist plz