CBSE Class 9 Answered
Expert Answer
Draw any quadrilateral as given in the question.
Now , as construction,
Draw AM perpendicular to BP
and
CN perpendicular to DP
We know that are of a triangle = 1/2* base * altitude
So,
LHS=
Area(triangle APB)*Area(triangle CPD)
=[(1/2)*BP*AM] [(1/2)DP*CN]
=[(1/2)*PD*AM] [(1/2)*BP*CN]
Area(triangle APD)* Area(triangle BPC)
=RHS
Hence proved.
Note that
for both trianglesAPB and ADP, AM is the height
Similarly
for both triangles CPD and BPC, CN is the height.
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