Geometry (C10)

In given figure ∠1 = ∠2 and ΔNSQ ≅ ΔMTR , then prove that ΔPTS ~ ΔPRQ.

 

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)