Question

Abcd is a parallelogram prove that ar bpc = ar dpq

Answer 1

ABCD is a parallelogram

Proof

ABCD is a parallelogram.

bc=cq

ar(triangle bpc)=ar(traingle dpq)

Explanation

first we need to join A to C

ar(triangle bpc) = ar (triangle apc)

so similarly,,

ar(triangle adc) = ar(triangle adq)

ar(triage adc)=ar(triangle adp)+ar(triangle apc)

ar(triangle adq)=ar(traingle adp)+ar(triangle dpq)

ar(triangle adc) = ar(triangle adq) &

ar(triangle adp) i===> common

ar(triangle apc) = ar(triangle dpq)

and

ar(triangle apc) = ar(triangle bpc)

so that,

ar(triangle bpc) = ar(triangle dpq)

Hence Proved!!!!