Question

THE MEDIANS BE & CF of a triangle ABC intersect at G . prove that area of triangle GBA = area of quadrilateral AFGE .

Answer 1

In a triangle
the line joining the mid-points of two sides of a triangle is parallel to the 3rd side
so, BC || EFtriangle on the same base and btw the same parallel lines are equal.
      
            Therefore, ar (BCF) = ar (BCE)                            =ar (BCG) + ar (CEG) = ar (BCG) + ar (BFG)                            =ar (CEG) = ar (BFG) ............................................1
The median of a triangle divides the triangle into two triangles
so, BE is median of ABCtherefore,       ar (BCE) = ar (ABE)                      = ar (BCG) + ar (CEG) = ar (BFG) + ar (AFGE)                 =ar (BCG) + ar (CEG) = ar (CEG) + ar (AFGE)............ (frm-1)                 = ar (BCG) = ar (AFGE)


                        Hence proved.




Hope it helped.....................