A point `O` inside a rectangle `A B C D` is joined to the vertices. Prove that the sum of the areas of a pair of opposite triangles so formed is equal to the sum of the other pair of triangles. Given: A rectangle `A B C D\ a n d\ O` is a point inside it. `O A ,\ O B ,\ O C\ a n d\ O D` have been joined. To Prove: `a r\ (A O D)+\ a r\ ( B O C)=\ a r\ ( A O B)+\ a r( C O D)`

A point O inside a rectangle A B C D is joined to the vertices. Prove that the sum of the areas of a pair of opposite triangles so formed is equal to the sum of the areas of other pair of triangles.

A point O inside a rectangle A B C D is joined to the vertices. Prove that the sum of the areas of a pair of opposite triangles so formed is equal to the sum of the other pair of triangles. GIVEN : A rectangle A B C D and O is a point inside it. O A ,O B ,O C and O D have been joined.. TO PROVE : a r(A O D)+a r( B O C)=a r( A O B)+a r( C O D) CONSTRUCTION : Draw E O F A B and L O M A Ddot

The vertices of a rectangle PQRS are joined from an interior point 'O'. Prove that the sum of the area of two opposite triangles so formed is equal to the sum of the areas of remaining two triangles

In a \ A B C , If L\ a n d\ M are points on A B\ a n d\ A C respectively such that L M B Cdot Prove that: a r\ (\ L O B)=a r\ (\ M O C)

A B C D is a parallelogram and O is any point in its interior. Prove that: (i) a r\ ( A O B)+a r\ (C O D)=1/2\ a r(A B C D) (ii) a r\ ( A O B)+\ a r\ ( C O D)=\ a r\ ( B O C)+\ a r( A O D)

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

In a \ A B C , If L\ a n d\ M are points on A B\ a n d\ A C respectively such that L M || B C . Prove that: a r\ (\ L O B)=a r\ (\ M O C) .

In a triangle \ A B C , If L\ a n d\ M are points on A B\ a n d\ A C respectively such that L M || B C . Prove that: a r\ (triangle \ L O B)=a r\ (triangle \ M O C)

Diagonals A C\ a n d\ B D of a trapezium A B C D with A B||D C intersect each other at O . Prove that a r\ ( A O D)=\ a r\ ( B O C) .

A B C D is a parallelogram whose diagonals intersect at Odot If P is any point on B O , prove that: a r\ ( A D O)=A R\ ( C D O) a r\ (\ A B P)=\ a r\ (\ C B P)