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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