A point P is taken on side CD of a parallelogram ABCD and CD is produced to Q making DQ=CP. the line through Q parallel to AD meet BP produced at S and AD is produced to meet BS at R . Prove that ARSQ is a parallelogram. Help me in 1 hour please..
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AQRS is a parallelogram point P is taken on side CD of a parallelogram ABCD and CD is produced to Q making DQ=CP
Step-by-step explanation:
in ΔQPS & Δ ABR
QP = AB ( QP = DQ + DP = CP + DP = DC = AB)
QS ║ AD
QP ║ AB ( as CD is extended to Q)
=> ΔQPS ≅ Δ ABR
QS = AR
PS = BR
PR + RS = BP + PR
=> BP = RS
QP = AB
QP ║ AB
=> ABPQ is a parallelogram
=> AQ= BP
=> AQ = RS
now in AQRS
QS = AR
AQ = RS
QS ║ AR
=> AQRS is a parallelogram
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