Question

In Fig. 10.23, PQRS is a square and SRT is an equilateral triangle. Prove that

(i) PT = QT

 (ii) ∠TQR = 15°

Answer 1

Given that PQRS is a square and SRT is an equilateral triangle. And given to prove that

(i) PT = QT

 (ii) ∠TQR = 15°

Now, PQRS is a square

So, by SAS congruence criterion we have

ΔTSP≅ΔTRQ

⇒PT=QT  [Corresponding parts of congruent triangles are equal]

Consider   ΔTQR ,

QR=TR     [From(3)]

ΔTQR is a isosceles triangle

⇒ ∠QTR= ∠TQR       [angles opposite to equal sides]

Now,

Sum of angles in a triangle is equal to 180°