Question

PQR is a equilateral triangle and QRST is a square.prove that:- PT=PS angle SR=15 degree

Answer 1

Since PQRS is a square and ∆ SRT is an equilateral triangle .

:- PST = 90 ° and TSR = 60°

PSR + TSR = 90° + 60°

PST = 150°

Similarly , we have PST and QRT , we have

Thus , in triangles PST and QRT , we have

PS = QR

PST = QRT = 150°

and , ST = RT

So , by SAS congruence criterion , we have

∆ PST ≈ ∆ QRT PT = QT

2) In ∆ TQR , we have

QR = RT

TQR = QTR = x ( say )

Now ,

TQR + QTR + QRT = 180° 2x + 150° = 180° x = 15° .