In a quadrilateral `A B C D` it is given tghat `A B||C D` nad the diagonals `A Ca n dB D` are perpendicular to each other. Show that `A DdotB CgeqA BdotC Ddot`

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 .

Is quadrilateral ABCD a rhombus ? I. Quadrilateral ABCD is a ||gm. II. Diagonals AC and BD are perpendicular to each other. The correct answer is : (a) /(b)/(c )/(d).

Find the area of the quadrilateral A B C D given in Figure. The diagonals A C and B D measure 48 m and 32 m respectively and are perpendicular to each other.

B D is one of the diagonals of a quadrilateral A B C Ddot\ \ A M\ a n d\ C N are the perpendiculars from A\ a n d\ C , respectively, on B Ddot Show That a r\ (q u a ddotA B C D)=1/2B Ddot(A M+C N)

In a cyclic quadrilateral A B C D if A B C D a n d /_B=70^0, find the remaining angles.

The two lines x=ay+b, z=cy+d and x=a'y+b', z=c'y+d' are perpendicular to each other, if

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.

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.

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)