Question

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

Answer 1

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)