Answer:
Proved.
Step-by-step explanation:
Given that coordinates of A, B and D are (0,0) (a,0) and (b,c) respectively
C is having y coordinate same as D but x coordinate will be a+b
(a+b,c) is C
Now the mid point of AC is using mid point formula
[tex](\frac{a+b}{2} ,\frac{c}{2} )[/tex]
to prove that the diagonals bisect each other it is sufficient to show that
The coordinates of the midpoint of diagonal BD=[tex](\frac{a+b}{2} ,\frac{c}{2} )[/tex]
Since we have B = (1,0) and D = (b,c)
using mid point formula we get mid point of BD
= [tex](\frac{a+b}{2} ,\frac{c}{2} )[/tex]
Comparing these two we find the mid point is the same for both the diagonals.
In other words, in a parallelogram diagonals bisect each other,
