Triangle ABC and parallelogram ABEF are on the same base, AB as in between the same parallels AB and EF. Prove that ar `(DeltaABC) = 1/2` ar(|| gm ABEF)

Triangle ABC and parallelogram ABEF ar on the same base, AB as in between the same parallels AB and EF. Prove that ar(DeltaABC)=1/2ar("||"gmABEF)

Prove by vector method, the parallelogram on the same base and in between the same parallel lines are equal in area.

In the figure, ΔABC and ΔABD are two triangles on the same base AB. If line segment CD is bisected by bar(AB) at O, show that ar (DeltaABC) = ar (DeltaABD).

Draw two triangles ABC and DBC on the same base and between the same parallels as shown in the figure with P as the point of intersection of AC and BD. Draw CE || BA and BF || CD such that E and F lie on line AD. Can you show ar(DeltaPAB) = ar(DeltaPDC) Hint : These triangles are not congruent but have equal areas.

Fill in the Blanks:The ratio of areas of a triangle and 9 par allelogram are on the base and between the same parallel lines is______

In the adjacent figure, triangle ABC and triangle DBC are on the same base BC. If AD and BC intersect at O, Prove that (area of triangle ABC )/(area of triangle DBC) = (AO) /(DO)

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

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

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

ABC is an isosceles triangle right angled at C. Prove that AB^2=2AC^2 .