E and F are respectively the mid-points of equal sides AB and AC of `DeltaABC` (see figure)
Show that BF = CE.

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

P and Q are the mid-points of the sides CA and CB respectively of a Delta ABC , right angled at C. Prove that 4(AQ^(2)+BP^(2))=5 AB^(2) .

If D and E, are the midpoints of the sides AB and AC of a triangle ABC, prove that vec(BE) +vec(DC)=(3)/(2)vec(BC).

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)

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) .

If D,E and F are the mid-points of the sides BC, CA and AB respectively of a triangle ABC and lambda is scalar, such that vec(AD) + 2/3vec(BE)+1/3vec(CF)=lambdavec(AC) , then lambda is equal to

D is a point on side BC of DeltaABC such that , angleADC=angleBAC . Show that AC^(2)= BCxxDC .

D, E, F are mid points of sides BC, CA, AB of Delta ABC . Find the ratio of areas of Delta DEF and Delta ABC .