Question

In the fig angle1 =angle2 and triangleNSQ congruent to MTR.prove that tri PTS SIMILAR TO TRI PRQ​

Answer 1

Answer:

Triangle MTR = Triangle NSQ

=> RT = QS ... (i)

It is given that

Angle 1 = Angle 2

=> PS = PT [ Sides opposite to equal angle are equal ] ... (ii)

From (i) and (ii)

PT/TR = PS/SQ

=> ST || QR [ By Converse of BPT ]

=> Angle 1 = Angle 3 and Angle 2 = Angle 4

[ Angle TQR = 3 and Angle SRQ = 4]

Thus is Triangles PST and PQR

Angle P = Angle P

Angle 1 = Angle 3

Angle 2 = Angle 4

So,by AAA criterion of similarity

Triangle PSQ = PQR.