ABC is a triangle and P any point on BC. If `barPQ` is the sum of `barAP + barPB + barPC`; show that `ABQC` is a parallelogram and `Q` therefore; is a fixed point.

ABC is a triangle and P any point on BC.if vec PQ is the sum of vec AP+vec PB+vec PC ,show that ABPQ is a parallelogram and Q, therefore,is a fixed point.

IN any /_\ABC, a point p is on the side BC. If vec(PQ) is the resultant of the vectors vec(AP) , vec(PB) and vec(PC) the prove that ABQC is a parallelogram and hence Q is a fixed point.

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

In triangle ABC, AB gt AC and D is any point on BC. Prove that, AB gt AD.

D,E and F are respectively the mid-points of the sides BC,CA and AB of a /_ABC. Show that (i) BDEF is a parallelogram

ABC is a triangle in which AB=AC and D is any point in BC. Prove that AB^(2)-AD^(2)=BDCD

ABCD is a parallelogram.P is a point on AD such that AP=(1)/(3)AD and Q is a point on BC such that CQ=(1)/(3)BP. Prove that AQCP is a parallelogram.

D is a point on side BC of triangle ABC such that AD = AC (see figure). Show that AB gt AD .

squareABCD is a parallelogram. P is any point on side BC. Find two pairs of triangles with equal areas.