Question

Δ PQR and Δ SQR are two isosceles triangles on the same base QR and vertices P and S are on

the same side of QR (see Fig.). If PS is extended to intersect QR at T, show that

(i) Δ PQS  Δ PRS

(ii) Δ PQT  Δ PRT

(iii) PT bisects P as well as S.
​

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)

SP/PQ= PR/QR = SR/PR

(Properties of similar triangles)

⇒ 8cm/SP= 3cm/6cm

⇒SP=4cm and

⇒ QR/6cm=6cm/3cm

⇒QR=12cm

III)

ar(△SPR)/ar(△PQR)

= SPsq/PQsq

= 4sq/8 sq

=4