2. ABCD is quadrilateral E, F, G and H are the midpoints of AB, BC, CD

1.	2. ABCD is quadrilateral E, F, G and H are the midpoints of AB, BC, CD and DArespectively. Prove that EFGH is a parallelogram
Answer» Given, quadrilateral ABCD E,F,G,H are mid pointsTo Prove, EFGH is a parallelogram. Proof, Join AC and BD, In ∆ADC H is mid point of AD and G is mid point of DC. So by mid point theorem, HG \|\| AC and HG= AC/2.......(1) Similarly, EF \|\|AC and EF =AC/2........(2) By (1) & (2), HG \|\| EF and HG=AF We know,If in a quadrilateral opposite sides are equal and parallel then it is a parallelogram. Hence proved.

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

Answer»

Given, quadrilateral ABCD E,F,G,H are mid pointsTo Prove, EFGH is a parallelogram.

Proof,

Join AC and BD,

In ∆ADC

H is mid point of AD and G is mid point of DC.

So by mid point theorem,

HG || AC and HG= AC/2.......(1)

Similarly,

EF ||AC and EF =AC/2........(2)

By (1) & (2),

HG || EF and HG=AF

We know,If in a quadrilateral opposite sides are equal and parallel then it is a parallelogram.

Hence proved.