In the Fig. AD and BE are medians of `DeltaABC and BE"||"DF`. Prove that `CF=(1)/(4)AC.`

ABCD is trapezium with AB || DC. The diagonal AC and BD intersect at E . If Delta AED ~ Delta BEC . Prove that AD = BC .

BL and CM are medians of a triangle ABC right angled at A. Prove that 4(BL^(2)+ CM^(2))=5BC^(2)

If ABCD is a quadrilateral and E and F are the midpoints of AC and BD respectively, then prove that vec(AB)+vec(AD)+vec(CB)+vec(CD)=4vec(EF) .

In squareABCD is a quadrilateral. M is the midpoint of diagonal AC and N is the midpoint of diagonal BD. Prove that : AB^(2)+BC^(2)+CD^(2)+DA^(2)=AC^(2)=AC^(2)+BD^(2)+4MN^(2).

Let ABC be an acute- angled triangle and AD, BE, and CF be its medians, where E and F are at (3,4) and (1,2) respectively. The centroid of DeltaABC , G(3,2) . The coordinates of D are

Find the coordinates of points Q and R on medians BE and CF respectively such that BQ:CF =2:1 and CR:RF =2:1​

Two triangles, DeltaABC" and "DeltaDBC, lie on the same side of the base BC. From a point P on BC, PQ||AB" and "PR||BD are drawn. They intersect AC at Q DC at R. Prove that QR||AD.

Point D and E are the points on sides AB and AC such athat AB = 5.6 , AD = 1.4 , AC =7.2 and AE = 1.8 . Show that DE||BC.