•Q Long-answer questions = = P. S - 2. In the given figure, PQ = PR = 5.2 cm and QS = SR = 2 cm. Are APQS and APRS congruent? If yes, then by which rule? List the corresponding elements of these triangles.
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Step-by-step explanation:
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)
⇒
SP
8cm
=
3cm
6cm
⇒SP=4cm and
⇒
6cm
QR
=
3cm
6cm
⇒QR=12cm
(III)
ar(△SPR)
ar(△PQR)
=
SP
2
PQ
2
=
4
2
8
2
=4
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