Question

In figure, angle 1 = angle 2 and triangle NSQ is congruent to triangle MTR, then prove that triangle PTS us similar to triangle PRQ

Answer 1

here it is

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Answer 2

Answer:In figure triangle NSQ≅ triangle MTR

Therefore,∠SQN=∠TRM

i.e., PQ=PR        (sides opposite to equal angles are equal )    ...............1

And already it is given that ∠1=∠2

I.e.,PS=PT         (sides opposite to equal angles are equal )     .............2

Subtracting 2 from 1 we get QS=TR

Therefore ST∥QR

Now as  ST∥QR  Therefore ∠1=∠SQR and ∠2=∠TRQ      (corresponding angles)

And therefore ∠SPT=∠QPR

Then by AAA similarity criteria Triangle PTS∼ triangle PRQ.

Step-by-step explanation: