Question

in the given figure, angle PQR =40°,angle PRQ = 20°,angle SQR = 20°.prove that ΔPQR =~ ΔRQS.
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Answer 1

Data:

∠PQR=∠PRQ

To prove:

∠PQS=∠PRT

According to the question,

∠PQR+∠PQS=180   ____________∣ Linear Pair

⇒∠PQS=180  −∠PQR--- (i)

Also ∠PRQ+∠PRT=180 __________ ∣ Linear Pair

⇒PRT=180  −∠PRQ

⇒∠PRQ=180 −∠PQR−−−(ii)(∠PQR=∠PRQ)

From (i) and (ii),

∠PQS=∠PRT=180  −∠PQR

∴∠PQS=∠PRT    [hence proved]