P is the mid-point of side AB of parallelogram ABCD. A line drawn from B parallel to PD meets CD at Q and AD produce at R. Prove that :
(i) AR = 2BC (ii) BR= 2BQ

Explanation

In `DeltaARB,P` is the mid-point of AB and PD is a parallel to BR.
`therefore` D will be the mid-point of AR.
`i.e." "AR=2AD`
But ABCD is a parallelogram.
`{:(therefore,AD=BC),("Therefore,",AR=2BC):}`
Which is part (i).
`squareABCD` is a parallelogram.

`{:(implies,DC"||"AB),(implies,DQ"||"AB):}`
In `DeltaRAB`
D is the mid-point of RA.
and `DQ"||"AB`
`therefore` Q is the mid-point of RB.
`implies" "BR=2BQ`
which is part (ii)