Q. 224.6( 7 Votes )

In the give figure, X and Y are the midpoints of AC and AB respectively, QP BC and CYQ and BXP are straight lines. Prove that ar(∆ABP) = ar(∆ACQ).


Answer :

Given: X and Y are the midpoints of AC and AB respectively, QP BC and CYQ and BXP are straight lines.


Construction: Join QB and PC


In Quadrilateral BCQP


Area (Δ QBC) = Area (Δ BCP) (Triangles on same base BC and between same parallel lines are equal in area) –1 and,


Area (||gm ACBQ) = Area (||gm ABCP) (parallelograms on same base BC and between same parallel lines are equal in area) –2


Subtract –1 from –2


Area (||gm ACBQ) – Area (Δ QBC) = Area (||gm ABCP) – Area (Δ BCP)


Area (∆ACQ) = Area (∆ABP)


Area(∆ABP) = Area(∆ACQ)


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