ABCD is a parallelogram X and Y are midpoints of BC and CD respectively. Prove that ar(triangle AXY)= 3/8 ar(parallelogram ABCD)
Asked by Sthitaprajna Mishra | 4th Feb, 2014, 08:11: PM
Consider the following figure.
Join the diagonals AC and BD to bisect at O.
OY produced meets AB at M and OX produced meets AB at N.
Since O and Y are the midpoints of AC and CD, we have
Thus, we have OY = CX
Therefore OXCY is a parallelogram.
Since parallelograms with the same base and between the same parallels are of equal areas, we have
Also, we have
Now consider the traingle CXY.
Since Y is the midpoint of CD, we have,
In the same way,
Now consider the area of the parallelogram ABCD.
Answered by | 6th Feb, 2014, 12:10: PM
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