Answer :

Given:

SQ and SR are bisectors of ∠Q and ∠R which meet at S

PQ > PR

To Prove: SQ > SR

Proof:

PQ > PR

∠PRQ > ∠PQR [angle opposite to longer side is larger] …………(1)

SQ and SR are bisectors of ∠Q and ∠R

∴ ∠SQR = 1/2 ∠PQR and ∠SRQ = 1/2 ∠PRQ

Dividing (1) by 1/2 we get

1/2 ∠PRQ > 1/2 ∠PQR

⇒ ∠SRQ > ∠SQR

⇒ SQ > SR [sides opposite to greater angle is longer]

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