ABCD is a quadrilateral and BD is one of its diagonals as shown in figure. Show that ABCD is a parallelogram and find its area.

 

4

(a)

In the figure, diagonals AC and BD of a trapezium ABCD with AB || CD intersect each other at O. Show that ar (\(\Delta \) AOD)= ar(\(\Delta \) BOC).

4

(a)

Prove that the area of a trapezium is equal to half of the product of its height and sum of parallel sides.

4

(a)

The diagonals of a parallelogram ABCD intersect at a point O. Through O, a line is drawn to intersect AD at P and BC at Q. Show that PQ divides the parallelogram into two parts of equal area.

4

(a)

\(\Delta \)ABC and \(\Delta \) ABD are two triangles on the same base AB. If line segment CD is bisected by AB at O, show that ar (\(\Delta \) ABC) = ar (\(\Delta \)ABD)

4

(a)

Prove that the diagonals of a rectangle are equal in length.

4

(a)

ABCD is a rectangle. E, F, G and H are mid-point of sides AB. BC, CD and DA, respectively. If ar(EFGH)=16 cm², find ar (ABCD).

4

(a)

PQRS is a parallelogram and O is a point in the interior of the parallelogram. Show that ar(POS) + ar(QOR)=\(\frac { 1 }{ 2 } ar(PQRS)\).

4

(a)

In \(\Delta\)ABC, E is the mid-point of median AD. show that ar(\(\Delta\)BED) = \(\frac { 1 }{ 4 } ar(\Delta ABC)\)

4

(a)

A villager had a plot of land in the shape of a quadrilateral. The Gram Panchayat decided to take come portion of his plot from one of the corners to construct a Health Centre. He reluctantly agrees but with a condition that he will be given equal amount of land in lieu of his plot so as to form a triangular plot.
Answer the following questions:
(i) Explain how could this be implemented with figure?
(ii) what value of the villager is depicted hare?
(iiii) Do you thick constructing a Health Centre in the village is justified.If so, why? 

4

(a)