In parallelogram abcd, e is the midpoint of
ab
and f is the midpoint of
dc
. let g be the intersection of the diagonal
db
and the line segment
ef
. prove that g is the midpoint of
ef.
△egb = △
by reason

Step-by-step explanation:

Example:

If E, F, G and H are respectively the mid-points of the sides of a parallelogram ABCD shows that ar ( EFGH) = 1/2 ar ( ABCD)

If E, F, G and H are respectively the mid-points of the sides of a parallelogram ABCD show that ar (EFGH) = 1/2 ar (ABCD)

Given: A parallelogram ABCD where E, F, G, H are the mid-points of AB,BC,CD & AD respectively

To prove: ar (EFGH) = 1/2 ar (ABCD)

Proof: Join H & F

Now,

So, AD || BC                  ( Opposite sides of parallelogram are parallel)

> DH || CF                     ( Parts of parallel lines are parallel)

Also, AD = BC               ( Opposite sides of parallelogram are equal)

1/2AD = 1/2 BC

DH = CF

( H is mid-point of AD

 F is mid-point of BC)

3x^3-x^2+6x-9