In given figure ∠1 = ∠2 and ΔNSQ ≅ ΔMTR , then prove that ΔPTS ~ ΔPRQ.
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∠ SQN = ∠ TRM (CPCT as ΔNSQ ≅ ΔMTR)
Since, ∠P + ∠1 + ∠2 = ∠P + ∠PQR + ∠PRQ (Angle sum property)
∠1 + ∠2 = ∠PQR + ∠PRQ
2∠1 = 2∠PQR (as ∠1 = ∠2 and ∠PQR = ∠PRQ)
∠1 = ∠PQR
Also, ∠2 = ∠PRQ
And ∠SPT = ∠QPR (common)
ΔPTS ~ ΔPRQ (By AAA similarity criterion)
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