Question

An equilateral triangle TSR is to be drawn on base SR of square g Quadrilateral PQRS, Where will point T lie? ​

Answer 1

Answer:

Because PQRS  is a square

∠PSR=∠QRS=90∘

Now In △SRT

  ∠TSR=∠TRS=60∘

∠PSR+∠TSR=∠QRS+∠TRS

⟹∠TSP=∠TRQ

Now in △TSP and △TRQ

                       TS=TR

                   ∠TSP=∠TRQ

               PS=QR

Therefore , △TSP≡△TRQ

     So  PT=QT

 

(ii)                Now in △TQR,

TR=QR(RQ=SR=TR)

∠TQR=∠QTR

And ∠TQR+∠QTR+∠TRQ=180

⟹∠TQR+∠QTR+∠TRS+∠SRQ=180

⟹2(∠TSR)+60+90=180  (∠TSR=∠QTR)

2(∠TSR)=30

⟹∠TSR=15∘