Question

P is the mid-point of side AB of a parallelogram ABCD.A line through B parallel to PD meets DC in Q and AD produced at R.Prove that:(i)AR=2BC and (ii)BR=2BQ. Well to be honest I really don't expect good answers from you guys.In fact I think there will be much more ignorance from your side but pls help me.

Answer 1

P is the mid - point of side AB of a parallelogram ABCD. A line through B parallel to PD meets DC at
Q and AD produced at R (see figure). Prove that :

(i) AR = 2BC
(ii) BR = 2BQ

(i) In △ARB,P is the mid point of AB and PD || BR.
∴ D is a mid - point of AR [converse of mid - point theorem]
∴ AR = 2AD 
But BC = AD [opp sides of ||gm ABCD]
Thus, AR = 2BC
(ii) ∴ ABCD is a parallelogram
∴ DC || AB ⇒ DQ || AB
Now, in △ARB,D is a mid - point of AR and DQ || AB 
∴ Q is a mid point of BR [converse of mid - point theorem]
⇒ BR = 2BQ

Answer 2

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