Question

In the given figure, if angle1 = angle 2 and triangleNSQ = triangleMTR, then
prove that trianglePTS similar to trianglePRO.
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Answer 1

∠SQN=∠TRM(CPCT as ΔNSQ≅ΔMTR)

Since,∠P+∠1+∠2=∠P+ΔPQR+ΔPQR(angle sum property)

∠1+∠2=ΔPQR+ΔPRQ

2∠1=2ΔPQR[as ∠1=∠2 and ΔPQR=ΔPRQ]

∠1=ΔPQR

Also,∠2=ΔPRQ

And ΔSPT=ΔQPR(common)

ΔPTSΔ~ΔPRQ(by AAA similarity criterion)