Question

In triangle PSR there is a point on line SR which is Q which is join to P. Q is point on SR such that PQ IS EQUAL TO PR,then prove that PS Is greater than PR​.​

Answer 1

Answer:

PQ=PR

then <PQR=PRQ

<PQR><PQS

<PRQ=<PSQ

ps>pr

Answer 2

Given: in ΔPSR, Q is a point on the side SR such that PQ = PR.

In ΔPRQ,

PR = PQ (given)

⇒ ∠PRQ = ∠PQR (opposite angles to equal sides are equal)

But ∠PQR > ∠PSR (exterior angle of a triangle is greater than each of opposite interior angle)

⇒ ∠PRQ > ∠PSR

⇒ PS > PR (opposite sides to greater angle is greater)

⇒ PS > PQ (as PR = PQ)