Question

$P$ 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 $R$. Prove that $AR=2BC$

Answer 1

Since PD || BQ or BR where P is mid point at AB therefore by theorem we get that,

D is also mid mid point on side AR of ∆ABR.

Hence, AD = DR

AD + DR = AR

AD + AD = AR

2AD = AR.

Since AD = BC ( opp. sides of ||gm are equal )

Therefore, 2BC = AR.