In the figure D, E are points on the sides AB and AC respectively of `DeltaABC` such that `ar(DeltaDBC) = ar(DeltaEBC)` . Prove that DE || BC.

P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD show that ar(DeltaAPB) = ar Delta(BQC)

D and E are points on the sides CA and CB respectively of a DeltaABC right angled at C. Prove that AE^(2)+BD^(2)= AB^(2)+DE^(2) .

In DeltaABC , E and F are the midpoints of sides AB and AC respectively. If EF=5cm, find BC.

In the figure, ΔABC, D, E, F are the midpoints of sides BC, CA and AB respectively. Show that (i) BDEF is a parallelogram (ii) ar(DeltaDEF)=1/4ar(DeltaABC) (iii) ar(BDEF)=1/2ar(DeltaABC)

In DeltaABC , D and E are points on the sides AB and AC respectively such that DE||BC . If AB= 6.75 cm, AC= 8.50 cm" and "EC = 6.80 cm . Then find BD.

In DeltaABC, /_B=90^(@) . D and E are any points on sides AB and BC respectively. Prove that AE^(2)+CD^(2)= AC^(2)+DE^(2) .

In the given figure, D is a point on side BC of DeltaABC such that (BD)/(CD)=(AB)/(AC) . Prove that AD is the bisector of /_BAC .

if D,E and F are the mid-points of the sides BC,CA and AB respectively of the DeltaABC and O be any points, then prove that OA+OB+OC=OD+OE+OF

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

In the given figure, A, B and C are points on OP, OQ and OR respectively such that AB||PQ" and "AC||PR . Show that BC||QR .