Question

In the given figure,∆PQR is right angled
at P, and PS | QR. If ✓Q = 45°. Find
(i) ✓QPS, (ii) ✓RPS,
(iii) ✓PRQ​

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)

⇒

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

Answer 2

Answer:

(i) 45° (ii) 45° (iii) 45°

Step by step answer:

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