Question

In trianglePQR,median PS is produced to point T such that PS=ST.Prove that PQTR is a parallelogram

Answer 1

Step-by-step explanation:

PQTR is a parallelogram

PS is median

=> QS = SR

PS = ST given

Comparing Δ PSR & Δ TSQ

PS = TS

SR = SQ

∠PSR = ∠TSQ  ( vertically opposite angles)

=> Δ PSR ≅ Δ TSQ

=> QT = PR

& ∠QTS = ∠RPS  

=> ∠QTP = ∠RPT

=> QT ║ PR

Similarly

ΔPSQ ≅ ΔTSR

=> PQ = RT

& ∠QPS = ∠RTS

=> ∠QPT = ∠RTP

=> PQ ║ RT

QT ║ PR &  PQ ║ RT

QT = PR  &  PQ = RT

=> PQTR is a parallelogram

QED

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