State whether the statement is true or false.If PQRS is a square and SRT is an equilateral triangle then PT = QT.

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State whether the statement is true or false.

If PQRS is a square and SRT is an equilateral triangle then PT = QT.

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True

False

answer is A.

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Detailed Solution

Given, PQRS is a square and SRT is an equilateral triangle.
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Since PQRS is a square, ∠PSR = ∠QRS = 90°.
In

△ SRT

, ∠TRS = 60°.
Now, ∠PSR + ∠TSR = ∠QRS + ∠TRS

\Rightarrow

∠TSP = ∠TRQ
Consider

△ TSP

and

△ TRQ

.
∠TSP = ∠TRQ (From above calculation)
TS = TR (Since

△ SRT

is an equilateral triangle)
PS = QR (Since PQRS is a square)
So,

△ TSP ⩭ △ TRQ

[By SAS congruence rule].
Thus, PT = QT since the two triangles are congruent.
Hence, the given statement is true and the correct option is 1.

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