Question

in parallelogram ABCD, E and F are the midpoints of sides AB and CD respectively. Show that the line segment AF and EC trisect the diagonal BD.

Answer 1

Please see the attachment

Answer 2

Thank you for asking this question. Here is your answer:

AE = EB = AB

and DF= FC = DC

but AB = DC

AEFD and BCFE are parallelogram AD

EF BC this will be an equation 1

Now In ∆ ABG

AE = EB and EX AG (from equation 1)

X is the mid point of GB

and in ∆ GBH

GX = XB

and XP BH

P is the mid point of GH

GP = PH

If there is any confusion please leave a comment below.