, QS and RT are bisectors of <Q and <R of an isosceles APQR with PQ-PR

1.	, QS and RT are bisectors of <Q and <R of an isosceles APQR with PQ-PR. Prove thatQS=RT.
Answer» Here PQ = PR ( Isosceles triangle ) , so from base angle theorem we get∠PQR =∠PRQ , So ∠TQR =∠SRQ------- ( 1 ) ( As∠PQR =∠TQR and∠PRQ =∠SRQ )And ∠TRQ =∠SQR -------- ( 2 ) ( Given QS and RT are bisectors of∠PQR and∠PRQ respectively )In ,∆TQR and∆SRQ ∠TQR =∠SRQ ( From equation 1 )QR = QR( Common side )And∠TRQ =∠SQR ( From equation 2 )So,∆TQR≅∆SRQ( By ASA rule ) Therefore , QS = RT ( By CPCT ) ( Hence proved )

, QS and RT are bisectors of <Q and <R of an isosceles APQR with PQ-PR. Prove thatQS=RT.

Answer»

Here PQ = PR ( Isosceles triangle ) , so from base angle theorem we get∠PQR =∠PRQ , So

∠TQR =∠SRQ------- ( 1 ) ( As∠PQR =∠TQR and∠PRQ =∠SRQ )And

∠TRQ =∠SQR -------- ( 2 ) ( Given QS and RT are bisectors of∠PQR and∠PRQ respectively )In ,∆TQR and∆SRQ

∠TQR =∠SRQ ( From equation 1 )QR = QR( Common side )And∠TRQ =∠SQR ( From equation 2 )So,∆TQR≅∆SRQ( By ASA rule )

Therefore ,

QS = RT ( By CPCT ) ( Hence proved )