Question

Given triangle PQR ,PS is perpendicular QR. PS²=QS×RS. Prove that triangle PQR is a right angled triangle..

Answer 1

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Here we have,

Right angled Triangle,

PSQ and PSR

Here we get 2 Equations :-

PQ² = PS² + QS²…………(1)

Also we have,

PR² = PS² + SR²………(2)

Here we have to add (1) and (2) we get

PQ² + PR² = 2PS² + QS² + SR²

According to Information

PS² = QS × RS

PQ² + PR² = 2(QS × SR) + QS² + SR²

PQ² + PR² = (QS + SR)²

Using Identity :-

(a + b)² = a² + b² + 2ab

PQ² + PR² = QR²        (QR = QS + SR)

Therefore,

∆PQR is a right angled triangle

Answer 2

Answer:

Here we have,

Right angled Triangle,

PSQ and PSR

Here we get 2 Equations :-

PQ² = PS² + QS²…………(1)

Also we have,

PR² = PS² + SR²………(2)

Here we have to add (1) and (2) we get

PQ² + PR² = 2PS² + QS² + SR²

According to Information

PS² = QS × RS

PQ² + PR² = 2(QS × SR) + QS² + SR²

PQ² + PR² = (QS + SR)²

Using Identity :-

(a + b)² = a² + b² + 2ab

PQ² + PR² = QR²        (QR = QS + SR)

Therefore,

∆PQR is a right angled triangle

Step-by-step explanation: