If `P` is any point in the interior of a parallelogram `A B C D` , then prove that area of the triangle `A P B` is less than half the are of parallelogram.

If P is any point in the interior of a parallelogram A B C D , then prove that area of the triangle A P B is less than half the area of parallelogram.

P is any point in the interior of a triangle ABC. Prove that : PA+PB lt AC +BC

P is any point in the interior of a triangle ABC. Prove that : PA+PB lt AC +BC

O is any point on the diagonal B D of the parallelogram A B C D . Prove that a r( triangle O A B)=a r(triangle O B C)

If a triangle and a parallelogram are on the same base and between the same parallels, then prove that the area of the triangle is equal to half the area of the parallelogram.

O is any point on the diagonal B D of the parallelogram A B C D . Prove that a r( /_\O A B)=a r( /_\O B C)

In a parallelogram A B C D , prove that sum of any two consecutive angles is 180^0dot

O' is any point on diagonal AC of a parallelogram ABCD. Prove that : area of Delta AOD = " area of " Delta AOB

E , F , G , H are respectively, the mid-points of the sides of parallelogram A B C D . Show that the area of EFGH is half the area of the parallelogram, A B C Ddot GIVEN : A quadrilateral A B C D in which L ,F ,G ,H are respectively the mid-points of the sides A B ,B C ,C D and D Adot TO PROVE : a r(^(gm)E F G H)=1/2a r(^(gm)A B C D) CONSTRUCTION : Join H and F

ABCD is a parallelogram. P and Q are the mid-points of sides AB and AD reapectively. Prove that area of triangle APQ= (1)/(8) of the area of parallelogram ABCD.