Question

in the given figure angle PQR = angle SRQ and anglePRQ = angle SQR prove that PQ = RS​

Answer 1

Step-by-step explanation:

Given:∠PQR = ∠PRQ

To prove:

∠PQS = ∠PRT

Proof:

∠PQR + ∠PQS  = 180° (by Linear Pair axiom)

∠PQS = 180° –  ∠PQR — (i)

∠PRQ + ∠PRT= 180° (by Linear Pair axiom)

∠PRT = 180° – ∠PRQ — (ii)

∠PRQ = 180° –  ∠PQR           [∠PQR = ∠PRQ]

From (i) and (ii), we can conclude the following,

∠PQS = ∠PRT= 180° – ∠PQR

∠PQS = ∠PRT

Hence, pq=ps

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