Question

2. ABCD i quadrilateral E, F, G and H are the midpoints of AB, BC, CD and DA respectively. Prove that EFGH is a parallelogram. ​

Answer 1

Given ABCD is a quadrilateral E,F,G,H are the midpoint of AB,BC,CD,DA respectively

In ΔADC

H and G the mid point of AD and DC

∴GH∥AC

And GH= 1/2

AC

In ΔABC

E and F the mid point of AB and BC

$$\therefore EF\parallel AC$$

And EF= 1/2

AC

So EF=GH and EFIIGH

So the quadrilateral EFGH

Opposite sides are parallel and equal

Then EFGH is a parallelogram

solution