In the adjoning figure, D and E are the points on the sides AB and AC respectively of `Delta ABC` and area of `Delta BCE = " area of " Delta BCD`.
Prove that `DE ||BC`

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

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, 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 a Delta ABC, D, E and F are the mid-point of sides BC, CA and AB respectively. If area of Delta ABC = 16 cm^(2) , find the area of trapezium FBCE

In Delta ABC, D,E and F are mid-point of sides AB ,BC and AC respectively , Prove that AE and DF bisect each other.

In triangle ABC, D and E are mid-points of the sides AB and AC respectively. Through E, a straight line is drawn parallel to AB to meet BC at F. Prove that BDEF is a parallelogram. If AB = 16 cm, AC = 12 cm and BC = 18 cm, find the perimeter of the parallelogram BDEF.

In the figure, ABCD is a rectangle, and F and E are points on AB and BC respectively. The area of Delta DFB is 9 and the area of Delta BED is 24. What is the perimeter of the rectangle?

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.

Delta ABC and Delta DBC are on same base BC and their vertices A and D are on opposite sides of BC. It is given that: area of Delta ABC = " area of " Delta DBC Prove that BC bisects the line segment AD.

In the adjoning figure, ABCD is a parallelogram. Prove that : area of Delta BPC = " area of " Delta DPQ