In the figure PQRS is square and SRT is an equilateral triangle. prove that. 1. 2. PT=QT 3.
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It seems that the student wanted to ask more but he/she only asked to prove PT = PQ, which I tried to solve.
Solution:-
Since PQRS is a square
∠ PSR = ∠ QRS.... (Each 90°)
Now again in equilateral triangle SRT,
we have ∠ TSR = ∠ TRS (Each 60°)
∠ PSR + ∠ TSR = ∠ QRS + ∠ TRS
⇒ ∠ TSP = ∠ TRQ
Now, in Δ TSP and Δ TRQ, we have
TS = TR....(Sides of equilateral triangle)
∠ TSP = ∠ TRQ (Proved above)
PS = SR (Sides of square)
Δ TSP ≡ Δ TRQ
∴ PT = QT
Hence proved.
Solution:-
Since PQRS is a square
∠ PSR = ∠ QRS.... (Each 90°)
Now again in equilateral triangle SRT,
we have ∠ TSR = ∠ TRS (Each 60°)
∠ PSR + ∠ TSR = ∠ QRS + ∠ TRS
⇒ ∠ TSP = ∠ TRQ
Now, in Δ TSP and Δ TRQ, we have
TS = TR....(Sides of equilateral triangle)
∠ TSP = ∠ TRQ (Proved above)
PS = SR (Sides of square)
Δ TSP ≡ Δ TRQ
∴ PT = QT
Hence proved.
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