Question

In the figure angle qrs= angle psr and angle prq= angle psq. prove that qr=ps

Answer 1

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