In a quadrilateral `A B C D` , given that `/_A+/_D=90o` . Prove that `A C^2+B D^2=A D^2+B C^2` .

In A B C ,\ \ /_A=60o . Prove that B C^2=A B^2+A C^2-A B.A C .

In A B C , A D is a median. Prove that A B^2+A C^2=2\ A D^2+2\ D C^2 .

In Figure, diagonal A C of a quadrilateral A B C D bisects the angles A\ a n d\ C . Prove that A B=A D\ a n d\ C B=C D

Diagonals A C and B D of a quadrilateral A B C D intersect at O in such a way that a r( A O D)=a r( B O C) . Prove that A B C D is a trapezium.

Diagonals A C a n d B D of a quadrilateral A B C D intersect at O in such a way that a r ( A O D)=a r ( B O C)dot Prove that A B C D is a trapezium.

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)

Calculate the area of the quadrilateral A B C D as shown in Fig.33, given that B D=42\ c m , A C=28\ c m , O D=12\ c m and A C_|_B D .

In a parallelogram A B C D , the bisector of /_A also bisects B C at Xdot Prove that A D=2A B

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

In a quadrilateral ABCD,CO and DO are the bisectors of /_C and /_D respectively. Prove that /_COD=(1)/(2)(/_A+/_B)