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)`

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)

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 trapezium with A B || D C . A line parallel to A C intersects A B at X and B C at Y . Prove that a r( triangle A D X)=a r(triangle A C Y) .

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, A B C D is a trapezium in which A B||C D . Prove that: a r( triangle A O D)=a r( triangle B O C) .

In Figure, A B C D is a trapezium in which A B||D C .\ \ D C is produced to E such that C E=A B , prove that a r(triangle A B D)=a r (triangle B C E) . Construction: Draw D M\ on B A produced and B N_|_D C

In a parallelogram A B C D ,E ,F are any two points on the sides A B and B C respectively. Show that a r(triangle A D F)=a r( triangle D C E) .

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

If the medians of a triangle A B C intersect at G , show that a r( triangle A G B)=a r( triangle A G C)=a r( triangle B G C)=1/3a r( triangle A B C) . GIVEN : triangle A B C such that its medians A D ,B E and C F intersect at G . TO PROVE : a r(triangle A G B)=a r( triangle B G C)=a r(triangle A G C)=1/3a r(triangle A B C)