Give the significance of the terms B.O.D. and C.O.D.

How do organic substances cause water pollution ? Explain the term C.O.D. and B.O.D.

In Fig. 4.170, A B C D is a trapezium in which A B∥ D C and A B=2\ D C . Determine the ratio of the areas of A O B and C O D . (FIGURE)

A point O in the interior of a rectangle A B C D is joined with each of the vertices A ,\ B ,\ C and D . Prove that O B^2+O D^2=O C^2+O A^2

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)

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 figure, A B\ a n d\ C D are straight lines and O P\ a n d\ O Q are respectively the bisectors of angles /_B O D\ a n d\ /_A O C . Show that the rays O P\ a n d\ O Q are in the same line.

If O is a point in space, A B C is a triangle and D , E , F are the mid-points of the sides B C ,C A and A B respectively of the triangle, prove that vec O A + vec O B+ vec O C= vec O D+ vec O E+ vec O Fdot

If O is a point in space, A B C is a triangle and D , E , F are the mid-points of the sides B C ,C A and A B respectively of the triangle, prove that vec O A + vec O B+ vec O C= vec O D+ vec O E+ vec O Fdot

The diagonals of quadrilateral A B C D ,\ A C\ a n d\ B D intersect in O . Prove that if B O=O D , the triangles A B C\ a n d\ A D C are equal in area.

The diagonals of quadrilateral A B C D ,A C and B D intersect in Odot Prove that if B O=O D , the triangles A B C and A D C are equal in area. GIVEN : A quadrilateral A B C D in which its diagonals A C and B D intersect at O such that B O = O Ddot TO PROVE : a r( A B C)=a r( A D C)