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.

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.

In the figure D, E are points on the sides AB and AC respectively of DeltaABC such that ar(DeltaDBC) = ar(DeltaEBC) . Prove that DE || BC.

E and F are the mid - points of AB and AC respectively of DeltaABC . The st. line EF is extended to the point D such that EF = FD. Prove that ADCE is a parallelogram.

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

If D,E and F are the middle points of the sides BC,CA and AB of the DeltaABC , then AD+BE+CF is

D and E are the mid-points of AB and AC respectively of the DeltaABC. AP is the median of BC. AP intersects DE at Q. Prove that DQ = QE and AQ = QP.

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) .

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

In triangle A B C ,points D , Ea n dF are taken on the sides B C ,C Aa n dA B , respectively, such that (B D)/(D C)=(C E)/(E A)=(A F)/(F B)=ndot Prove that triangle D E F=(n^2-n+1)/((n+1)^2) triangle(A B C)dot

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