ABCD is a square. E, F, G and H are the mid points of `AB, BC, CD and DA` respectively. Such that `AE = BF = CG = DH`. Prove that EFGH is a square.

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

The points E, F , G and H are on the sides AB, BC , CD and DA respectively of the rectangle ABCD , such that AE = BF = CG = DH . Prove that EFGH is a parallelogram.

D, E and F are the mid-points of AB, BC and CA of the equilateral DeltaABC. Prove that DeltaDEF is also an equilateral triangle.

D, E and F are the mid-points of the sides AB, BC and CA of the DeltaABC . Prove that DeltaDEF=1/4DeltaABC .

If E, F G and H are respectively the midpoints of the sides AB, BC, CD and AD of a parallelogram ABCD, show that ar(EFGH) =1/2 ar (ABCD) .

ABCD is a quadrilateral . 3, 4, 5 and 6 points are market on the sides AB, BC, CD and DA respectively . The number of triangles with vertices on different slides is

D, E and F are the mid-points of the sides AB, AC and BC of the DeltaABC. Prove that DE and AF bisects each other.

Let ABCD is a square with sides of unit length. Points E and F are taken om sides AB and AD respectively so that AE= AF. Let P be a point inside the square ABCD.The maximum possible area of quadrilateral CDFE is-

Let ABCD is a square with sides of unit lenghts . Points E and F are taken on sides AB and AD respectively so that AE =AF . Let P be a point inside the square ABCD. The maximum area of quandrilateral CDFE will be -

D is the mid-point of BC of DeltaABC . E and O are the mid-points of BD and AE respectively. Then the area of the triangle BOE is-