Question

In a parallelogram ABCD,E and F are the mid points of sides AB and CD respectively.show that line segments AF and EC trisect the diagonal BD

Answer 1

the opposite sides are equal in a parallelogram.the opposite angles are equal too. F is the midpoint of CD when we join A and F ,E and  C.they form another parallelogram.as opposite sides are equal AE=FC.this divides the parallelogram into two congruent triangles and a parallelogram.the altitude of triangle EBC and ADF from B and D are equal if extended out of the triangle and measured we can find that diagonal bd is is trisect by AF and EC