Question

In the given figure angle1 =angles do triangle NSQ =~ triangle MTR , then prove that ∆PTS~∆PRQ

Answer 1

Answer:

HEY MATE SEE YOUR ANSWER

∠ 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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