`A B C D` is a rhombus and its diagonals intersect at `Odot`
Is ` B O C\ ~= D O C ?` State the congruence condition used?
Also state, if ` B C O= D C O`

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)

A B C D is a parallelogram whose diagonals A C and B D intersect at Odot A Line through O intersects A B at P and D C at Qdot Prove that a r( P O A)=a r( Q O C)dot

ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If /_D B C" "=" "70^o, /_B A C" "i s" "30^o , find /_B C D . Further, if A B" "=" "B C , find/_E C D .

A B C D is a cyclic quadrilateral whose diagonals A C\ a n d\ B D intersect at Pdot If A B=D C , prove that: P A B\ ~= P D C P A=P D\ a n d\ P C=P B (iii) A D B C

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 E 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)

If the diagonals A C ,B D of a quadrilateral A B C D , intersect at O , and seqarate the quadrilateral into four triangles of equal area, show that quadrilateral A B C D is a parallelogram. GIVEN : A quadrilateral A B C D such that its diagonals A C and B D intersect at O and separate it into four parts such that a r( A O B)=a r( B O C)=a r( C O D)=a r( A O D) TO PROVE : Quadrilateral A B C D is a parallelogram.

A B C D is a trapezium in which A B C D . The diagonals A C and B D intersect at O . Prove that (i) A O B C O D (ii) If O A=6c m , O C=8c m , Find: (A r e a ( A O B))/(A r e a ( C O D)) (b) (A r e a ( A O D))/(A r e a ( C O D))

A B C D is a parallelogram whose A C\ a n d\ B D intersect at Odot A line through O intersects A B\ a t\ P\ a n d\ D C\ at Qdot Prove that a r\ (\ P O A)=\ a r\ (\ Q O C)dot

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)

In Fig. 9.25, diagonals AC and BD of quadrilateral ABCD intersect at O such that O B" "=" "O D . If A B" "=" "C D , then show that: (i) a r" "(D O C)" "=" "a r" "(A O B) (ii) a r" "(D C B)" "=" "a r" "(A C B) (iii) D A" "||" "C