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Q.

Tell whether the following statement is true or false:

In the give figure, X and Y are the midpoints of AC and AB respectively, QP || BC and CYQ and BXP are straight lines. Then area of triangle ABP = area of triangle ACQ.

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a

True

b

False

answer is A.

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Detailed Solution

Given a figure in which X and Y are the midpoints of AC and AB respectively.
Question Image

Question Image

Since PQ || XY || BC,
Area of triangle CXY = Area of triangle BXY ---- 1
As, both are on same base and between parallel.
Similarly for quadrilateral,
Area of XYAQ = Area of XYAP ----- 2
Now from both equations 1 and 2,
Area of triangle CXY + Area of XYAQ = Area of triangle BXY + Area of XYAP
Area of triangle ABP = Area of triangle ACQ
Given statement is true.
Hence, option 1 is correct.

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