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

Since, POPS is a square and ∆SRT is an equilateral triangle.

∴ ∠PSR = 90° and ∠TSR = 60°

=> ∠PSR + ∠TSR = 90°+ 60°

=> ∠PST = 150°

Similarly, we have

∠QRT = 150°

Thus, in A PST and ∆ QRT, we have

PS = QR [sides of a square]

∠PST = ∠QRT = 150°

and ST = RT [sides of an equilateral triangle]

=> PT =QT