In Figure, `A B C D` is a quadrilateral and `B E || A C` and also `B E` meets `D C` produced at `E` . Show that area of `triangle A D E` is equal to the area of the quadrilateral `A B C D`.

In Figure, A B C D is a quadrilateral and B E|A C and also B E meets D C produced at Edot Show that area of A D E is equal to the area of the quadrilateral A B C D

In Figure, compute the area of quadrilateral A B C D .

In Figure, if A B C is an equilateral triangle. Find /_B D C\ a n d\ /_B E C

In Figure, A B C D E is a pentagon. A line through B parallel to A C meets D C produced at F . Show that: (i) a r( triangle A C B)=a r(triangle A C F) (ii) a r( quadrilateral A E D F)=a r(A B C D E)

If the diagonals A C ,\ B D of a quadrilateral A B C D , intersect at O , and separate the quadrilateral into four triangles of equal area, show that quadrilateral A B C D is a parallelogram.

A B C D is a cyclic quadrilateral. A Ba n dD C are produced to meet in Edot Prove that E BC ~EDAdot

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 quadrilateral. A line through D , parallel to A C , meets B C produced in P as shown in figure. Prove that a r (triangle A B P) =a r (Quad. A B C D) .

A B C D is a quadrilateral and B D is one of its diagonals as shown in Figure. Show that A B C D is a parallelogram and find its area.

In Figure, A B C D E\ is a pentagon. A line through B parallel to A C meets D C produced at F . Show that: (i) a r\ ( A C B)=a r\ ( A C F) (ii) a r\ (A E D F)=a r\ (A B C D E)