Question

Let ABCD be a quadrilateral and X be the midpoint of BD. Prove that the area of AXCB is one half the area of ABCD.
pls solve yaar dont just earn points​

Answer 1

Answer:

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