Question

In the given figure,PQRS is a square and SRT is an equilateral triangle.Prove that PT=QT.

Answer 1

Hope it will be helpful

Answer 2

Point T can be inside or outside the triangle.

In both cases, consider the triangles PTS and QTR. In them,

First consider ∠PST and ∠QRT

Case 1 : T is inside the square. Both angles are (90° - 60°) = 30°

Case 2 : T is outside the square. Both of the angles are equal to 90+60 = 150°.

PS=QR  (Both are sides of square PQRS)

ST = RT  (Both are sides of equilateral ΔSRT)

In both cases, by SAS congruency, ΔPTS ≅ ΔQTR.

Hence PT = QT (by CPCT)

PS  : Sorry I haven't uploaded a figure.