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.

K, L, M and N are points on the sides AB, BC, CD and DA respectively of a square ABCD such that AK = BL = CM = DN. Prove that KLMN is a square.

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 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 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 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 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.

D, E and F are the mid-points of the sides BC, CA and AB respectively of triangle ABC. Prove that: BDEF is a parallelogram.

P,Q,R and S are respectively the mid points of the sides AB,BC,CD and DA of a quadrilateral ABCD such that ACbotBD . Prove that PQRs is a rectangle.

ABCD is a quadrilateral; P,Q,R and S are the points of trisection of side AB,BC,CD and DA respectively and are adjacent to A and C; prove that PQRS is parallelogram.

In rectangle ABCD, E is the midpoint of side BC. Prove that, AE = DE.