P and Q are respectively the midpoints of sides AB and BC or a triangle ABC and R is the mid-point of AP, show ar(PRQ)=`1/2` ar(ARC).

P and Q are respectively the midpoints of sides AB and BC or a triangle ABC and R is the mid-point of AP, show ar(RQC) = 3/8 ar(ABC).

P and Q are respectively the midpoints of sides AB and BC or a triangle ABC and R is the mid-point of AP, show ar(PBQ)=ar(ARC).

D,E and F are respectively the mid points of the sides AB,BC and CA of a triangle ABC. Prove that by joining these mid points D,E and F and the triangle ABC is divided into four congruent triangles.

D, E and F are respectively the mid-points of the sides BC, CA and AB of a triangle ABC . Show that:- BDEF is a parallelogram.

ABCD is a squre. E and F are respectivley the mid-points of BC and CD. If R is the mid-points of EF. Prove that ar (AER) = ar(AFR).

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

D, E and F are respectively the mid¬ points of the sides BC, CA and AB of triangleABC . Determine the ratio of the areas of triangles DEF and ABC.

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

P,Q,R and S are respectively the mid points of the sides AB,BC,CD and DA of a quadrilateral ABCD such that ACbotBD . Prove that PQRs is a rectangle.