Prove that the area of a triangle is half the product of any its sides and the corresponding altitudes .
Construction: Trough C and A draw CP parallel to BA and AP parallel to BC, intersecting each other at P.
CP parallel to BA (By Construction)
AP parallel to BC (By Construction)
Therefore BCPA is a parallelogram.
Hence AC is a diagonal of parallelogram BCPA.
Therefore, area of triangle = ½ ar(IIgm BCPA) = ½ × BC × AD (As BC is the base and AD is the altitude of IIgm BCPA).