Question

in quadrilateral ABCD it is being given that M is the midpoint of AC prove that area of rectangle ABMD is equal to area of rectangle ABMD

Answer 1

Given that ABCD is a qudrilateral , M is the mid point  AC

To prove : ar DMBC = ar ABMD

Proof : In ABC , since M is the midpoint of AC, BM is the median.

ar ABM = ar CBM (the median divides the triangle into 2 triangles of equal areas).........(1)

In ADC , DM is the median.

ar ADM = ar CDM (the median divides the triangle into 2 triangles of equal areas).......( 2)

Adding (1) and (2)

ar ABM + ar ADM = ar CBM + ar CDM

ar ADMB = ar DMBC