in the given figure , abcd is a parallelogram.prove that ar(triangle bcp) = ar(triangle dpq), if bc=cq
given: ABCD is a parallelogram.
area(ΔBCP)=area(ΔAPC).............(1) [since PC is parallel to AB and the triangles formed between same set of parallel line and with same base are equal in areas]
similarly area(ΔADC)=area(ΔADQ) [the triangles have the same base AD and between the parallel lines of BQ and AD]
from (1) and (2)
hope this helps you.