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.

D, E and F are the mid-points of the sides BC, CA and AB, respectively of an equilateral Delta ABC. Show that Delta DEF is also an equilateral triangle.

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

In an equilateral triangle A B C if A D_|_B C , then

A D ,\ B E\ a n d\ C F , the altitudes of A B C are equal. Prove that A B C is an equilateral triangle.

A D ,\ B E\ a n d\ C F , the altitudes of A B C are equal. Prove that A B C is an equilateral triangle.

A point D is on the side B C of an equilateral triangle A B C such that D C=1/4\ B C . Prove that A D^2=13\ C D^2 .

In Figure, A B C is an equilateral triangle. Find m\ /_B E C

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

If D ,E ,F are the mid-points of the sides B C ,C Aa n dA B respectively of a triangle A B C , prove by vector method that A r e aof D E F=1/4(a r e aof A B C)dot

In DeltaA B C , D, E and F are respectively the mid-points of sides AB, BC and CA. Show that DeltaA B C is divided into four congruent triangles by joining D, E and F.