A diagonal of a parallelogram divides it into two triangles of equal area. GIVEN : A parallelogram `A B C D` in which `B D` is one of the diagonals. TO PROVE : ar `( A B D)=a r( C D B)`

Prove that A diagonal of a parallelogram divides it into two triangles of equal area.

Prove that two diagonals of a parallelogram divides it into four triangles of equal areas.

Show that the diagonals of a parallelogram divide it into four triangles of equal area. GIVEN : A parallelogram A B C D . The diagonals A C and B D intersect at Odot TO PROVE : a r( O A B)=a r( O B C)=a r( O C D)=a r( A O D)

Show that the diagonals of a parallelogram divide it into four triangles of equal area. GIVEN : A parallelogram A B C D . The diagonals A C and B D intersect at Odot TO PROVE : a r( O A B)=a r( O B C)=a r( O C D)=a r( A O D)

Show that a median of a triangle divides it into two triangles of equal area. GIVEN : A triangle A B C in which A D is the median. TO PROVE : a r(triangle A B D)=a r( triangle A D C) CONSTRUCTION : Draw A L_|_B C

Show that a median of a triangle divides it into two triangles of equal area. GIVEN : A A B C in which A D is the median. TO PROVE : a r( A B D)=a r( A D C) CONSTRUCTION : Draw A L_|_B C

If each diagonal of a quadrilateral separates it into two triangles of equal area then show that the quadrilateral is a parallelogram. GIVEN : A quadrilateral A B C D such that its diagonals A C and B D are such that a r( A B D)=a r( C D B ) and a r( A B C)=a r( A C D)dot TO PROVE: Quadrilateral A B C D is a parallelogram.

If each diagonal of a quadrilateral separates it into two triangles of equal area then show that the quadrilateral is a parallelogram. GIVEN : A quadrilateral A B C D such that its diagonals A C and B D are such that a r( A B D)=a r( C D B ) and a r( A B C)=a r( A C D)dot TO PROVE: Quadrilateral A B C D is a parallelogram.

A quadrilateral A B C D is such that diagonal B D divides its area in two equal parts. Prove that B D bisects A C . GIVEN : A quadrilateral A B C D in which diagonal B D bisects it. i.e. a r(triangle A B D)=a r(triangle B D C) CONSTRUCTION : Join A C Suppose A C and B D intersect at O . Draw A M_|_B D and C N _|_ B D . TO PROVE : A O=O C .

A quadrilateral A B C D is such that diagonal B D divides its area in two equal parts. Prove that B D bisects A Cdot GIVEN : A quadrilateral A B C D in which diagonal B D bisects it. i.e. a r( A B D)=a r( B D C) CONSTRUCTION : Join A C Suppose A C and B D intersect at O . Draw A L_|_B D and C M B Ddot TO PROVE : A O=O Cdot