In a parallelogram ABCD, E and F are the midpoints of the sides AB and DC respectively. Show that the line segments AF and EC trisect the diagonal BD.

In a triangle ABC, if D and E are mid points of sides AB and AC respectively. Show that vecBE+ vecDC=(3)/(2)vecBC .

In DeltaABC, D, E and F are the midpoints of sides AB, BC and CA respectively. Show that DeltaABC is divided into four congruent triangles, when the three midpoints are joined to each other. (ΔDEF is called medial triangle)

ABCD a parallelogram, and A_1 and B_1 are the midpoints of sides BC and CD, respectively. If vec(A A)_1 + vec(AB)_1 = lamda vec(AC) , then lamda is equal to

Let A, B, and C be the vertices of a triangle. Let D, E, and F be the midpoints of the sides BC, CA, and AB respectively. Show that vec(AD)+vec(BE)+vec(CF)=vec(0) .

In trigle ABC, the points D, E, F are the midpoints of the sides BC,CA, and AB respee. Tively. Using vector methed ,show that the area of Delta DEF is equal to (1)/(4) (area of ABC).

A B C D parallelogram, and A_1a n dB_1 are the midpoints of sides B Ca n dC D , respectivley . If vec AA_1+ vec A B_1=lambda vec A C ,t h e nlambda is equal to a. 1/2 b. 1 c. 3/2 d. 2 e. 2/3

In Delta ABC , D and E are points on the sides AB and AC respectively. For each of the following cases show that DE||BC (i) AB=12 cm , AD=8 cm, AE=12 cm and AC=18 cm. (ii) AB=5.6 cm, AD=1.4 cm, AC=7.2 cm and AE=1.8 cm.

ABCD is quadrilateral E, F, G and H are the midpoints of AB, BC, CD and DA respectively. Prove that EFGH is a parallelogram.

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.