In a triangle ABC (see figure), E is the midpoint of median AD, show that
(i) ar `DeltaABE = ar DeltaACE`
(ii) `ar DeltaABE=1/4ar(DeltaABC)`

PQRS and ABRS are parallelograms and X is any point on the side BR. Show that (i) ar(PQRS) = ar(ABRS) (ii) ar(DeltaAXS) =1/2 ar(PQRS)

ABCD is parallelogram and ABEF is a rectangle and DG is perpendicular on AB. Prove that (i) ar (ABCD) = ar(ABEF) (ii) ar (ABCD) = AB xx DG

In the given Figure AB and CD are intersecting at ‘O’, OA = OB and OD = OC. Show that (i) Delta AOD ~= DeltaBOC and (ii) AD || BC .

Let O be the circumcentre and H be the orthocentre of an acute angled triangle ABC. If A gt B gt C , then show that Ar (Delta BOH) = Ar (Delta AOH) + Ar (Delta COH)

In an isosceles triangle ABC with AB = AC, D and E are points on BC such that BE = CD (see figure) Show that AD = AE

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).

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).

In the figure , DE || BC and (AD)/(DB) = 3/5 , calculate the value of (i) ("area of " Delta ADE)/("area of " Delta ABC) (ii) ("area of trapezium BCED")/("area of " Delta ABC)