Question

In the following figure PQRS is a square and SRT is an equilateral triangle. Prove that
(i)Triangle PQTis an isosceles
(ii) Find Angle TPS

Answer 1

Step-by-step explanation:

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(∠TQR)+60+90=180 (∠TQR=∠QTR)

2(∠TQR)=30

⟹∠TQR=15

∘

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Answer 2

Answer:∠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(∠TQR)+60+90=180  (∠TQR=∠QTR)

2(∠TQR)=30

⟹∠TQR=15  

∘

   

Step-by-step explanation:

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