. In figure (4) PQR is an equilateral triangle and QRST is a square. Prove that
(i) PT = PS (ii) PSR = 15

Dear student,
Given:
Triangle PQR is an equilateral triangle, i.e., each angle is 60°.
QRST is a square, i.e., each angle is 90°.

PQT =PQR+TQR=60+90=150°
Similarly, PRS=150°
Consider the triangles PQT and PRS.

PQ = PR     (Sides of an equilateral triangle)QT = RS       (Sides of a square)PQT=PRS= 150°     (Proved)PQT PRS            (SAS criterion)PT = PS          (CPCT)

Further, the side of the square coincides with the triangle, PR = RS, which makes PRS isosceles.
Let PSR=SPR=x.
Using angle sum property of a triangle, we get:
150°+x+x=150°+2x=180°2x=30°x=15°

PSR = 15°
Hence, proved.
Regards

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