Question

A point p lies on the side CD of parallelogram ABCD . If ar (abcd) =56cm2 then ar (pab) = cm2

Answer 1

Answer:

Step-by-step explanation:

Question- 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 meets BP produced at S and AD is produced to meet BS at R. Prove that ARSQ is a parallelogram.

Solution

 QD=CP                          [ Given ]       ---- ( 1 )

 AB=CD                          [ Opposite sides of parallelogram ]

⇒  AB=CP+DP

⇒  AB=QD+DP                  [ From ( 1 ) ]

⇒  AB=QP

∴  AB∥QP                             [ Since, AB∥CD ]

∴  ABPQ is a parallelogram.

∴  AQ∥BP

As SR is extended part of BP

⇒  AQ∥SR

⇒  AQ∥RP

⇒  QS∥AR

∴  ARSQ is a parallelogram.