In the adjacent figure ABCD is a parallelogram and E is the midpoint of the side BC. If DE and AB are produced to meet at F, show that `AF = 2AB`.

ABCD is a parallelogram, E is the mid-point of AB and CE bisects angleBCD . Then angleDEC is

If D, E and F be the middle points of the sides BC,CA and AB of the DeltaABC , then AD+BE+CF is

If D is the midpoint of the side BC of a triangle ABC, prove that vec(AB)+vec(AC)=2vec(AD)

In the figure, ABC is a triangle in which AB= AC. Points D and E are points on the side AB and AC respectively such that AD=AE. Show that points B, C, E and D lie on a same circle.

In the figure, ABCD is a quadrilateral. AC is the diagonal and DE || AC and also DE meets BC produced at E. Show that ar(ABCD) = ar (DeltaABE).

squareABCD is a parallelogram. Point E is on side BC , line DE intersects Ray AB in point . T Prove that : DExxBE=CExxTE .

If D is the midpoint of the side AB of a triagle ABC prove that vec(BC)+vec(AC)=-2vec(CD)

In the adjacent figure, we have AC = XD, C and D are mid points of AB and XY respectively. Show that AB = XY.

ABCD is a rectangle and P,R and S are the mid - points of the AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.