D, E and F are respectively the mid-points of the sides BC, CA and AB of a`DeltaA B C`. Show that
(i) BDEF is a parallelogram.
(ii) `a r\ (D E F)=1/4a r\ (A B C)`
(iii) `a r\ (B D E F)=1/2a r\ (A B C)`

E and F are respectively the mid-points of equal sides AB and AC of DeltaA B C (see Fig. 7.28). Show that BF = C E .

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.

If E ,F ,G and H are respectively the mid-points of the sides of a parallelogram A B C D , show that a r(E F G H)=1/2a r(A B C D)

If E ,F ,G and H are respectively the mid-points of the sides of a parallelogram A B C D , show that a r(E F G H)=1/2a r(A B C D)dot

If E ,\ F ,\ G\ a n d\ H are respectively the mid-points of the sides of a parallelogram A B C D ,\ Show that a r(E F G H)=1/2a r\ (A B C D)

In Figure, D ,E and F are, respectively the mid-points of sides B C ,C A and A B of an equilateral triangle A B C . Prove that D E F is also an equilateral triangle.

In Figure, D ,E and F are, respectively the mid-points of sides B C ,C A and A B of an equilateral triangle A B C . Prove that D E F is also an equilateral triangle.

E , F , G , H are respectively, the mid-points of the sides A B ,B C ,C D and D A of parallelogram A B C D . Show that the quadrilateral E F G H is a parallelogram and that its area is half the area of the parallelogram, A B C Ddot GIVEN : A quadrilateral A B C D in which L ,F ,G ,H are respectively the mid-points of the sides A B ,B C ,C D and D Adot TO PROVE : (i) Quadrilateral E F G H is a parallelogram a r(||^(gm)E F G H)=1/2a r(||^(gm)A B C D) CONSTRUCTION : Join A C and H F

E , F , G , H are respectively, the mid-points of the sides A B ,B C ,C D and D A of parallelogram A B C D . Show that the quadrilateral E F G H is a parallelogram and that its area is half the area of the parallelogram, A B C Ddot

D ,\ E ,\ F are the mid-points of the sides B C ,\ C A and A B respectively of a Delta A B C . Determine the ratio of the areas of D E F and A B C .