D, E, F are the mid points of side AB, BC, AC prove that BDEF is a parallelogram whose area is half that of `Delta` ABC

Statement 1: ABC is given triangle having respective sides a,b,c. D,E,F are points of the sides BC,CA,AB respectively so that AFDE is a parallelogram. The maximum area of the parallelogram is 1/4 bcsinA. Statement 2 : Maximum value of 2kx--x^2 is at x = k.

In the given figure, D is mid-point of side AB of triangleABC and BDEC is a parallelogram. Prove that : Area of DeltaABC = Area of ////gmBDEC

In the given triangle P, Q and R are the mid points of sides AB, BC and AC respectively. Prove that triangle PQR is similar to triangle ABC.

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.

In Delta ABC , E is mid-point of side AB and EBCD is a parallelogram. If the area of Delta ABC is 80 cm, find the area of parallelogram EBCD.

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)

In the adjoining figure D, E and F are the mid-points of the sides BC, CA and AB respectively of Delta ABC . Prove that: (i) square BDEF is a parallelogram (ii) area of Delta DEF = (1)/(4) xx " area of " Delta ABC (iii) square BDEF = (1)/(2) xx " area of " Delta ABC

D and F are the mid-points of sides AB and AC of a triangle ABC. A line through F and parallel to AB meets BC at point E. Prove that BDFE is a parallelogram

D, E and F are the mid-points of the sides AB, BC and CA of an isosceles triangle ABC in which AB = BC. Prove that DeltaDEF is also isosceles.

D and F are the mid-points of sides AB and AC of a triangle ABC. A line through F and parallel to AB meets BC at point E. Find AB, if EF=4.8cm .