In a triangle PQR, side PQ is produced to S so that QS=RQ. If triangle PQR =60degree,and angle RPQ =70degree, prove that (1):PS>RS, (2):PS>PR
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10th
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Triangles
Criteria for Triangle Similarity
PQR is a triangle. S is a p...
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Asked on October 15, 2019 by
Mridula Thobhani
PQR is a triangle. S is a point on the side QR of ΔPQR such that ∠PSR=∠QPR/ Given QP=8cm, PR=6cm and SR=3cm.
(I) Prove ΔPQR∼Δ SPR
(II) Find the length of QR and PS
(III)
areaofΔSPR
areaofΔPQR
.
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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)
⇒
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
=
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