XY is a line parallel to side BC of a triangle ABC. If `B E\ ||\ A C`and `C F\ ||\ A B`meet XY at E and F respectively, show that `a r\ (A B E)\ =\ a r\ (A C F)`

X Y isa line parallel to side B C of A B CdotB E A and C F A B meet X Y in E and F respectively.Show that a r( A B E)=a r( A C F)dot

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( A D F)=a r( D C E)dot

In Figure, A B C D ,\ A B F E\ a n d\ C D E F are parallelograms. Prove that a r( A D E)=a r( B C F)

Any point D is taken in the base B C of a triangle A B C\ a n d\ A D is produced to E , making D E equal to A Ddot Show that a r\ ( B C E)=a r( A B C)

In Figure, A B C is a right triangle right angled at A ,\ B C E D ,\ A C F G\ a n d\ A M N are square on the sides B C ,\ C A\ a n d\ A B respectively. Line segment A X\ _|_D E meets B C at Ydot Show that: a r\ (C Y X E)=\ a r\ (A C F G)

In Figure, A B C is a right triangle right angled at A ,\ B C E D ,\ A C F G\ a n d\ A M N are square on the sides B C ,\ C A\ a n d\ A B respectively. Line segment A X\ _|_D E meets B C at Ydot Show that: a r(C Y X E)=a r\ (A C F G)

In Figure, A B C is a right triangle right angled at A ,\ B C E D ,\ A C F G\ a n d\ A M N are square on the sides B C ,\ C A\ a n d\ A B respectively. Line segment A X\ _|_D E meets B C at Ydot Show that: a r\ (C Y X E)=2a r(\ F C B)

Let A B C be an isosceles triangle with A B=A C and let D ,\ E ,\ F be the mid points of B C ,\ C A\ a n d\ A B respectively. Show that A D_|_F E\ a n d\ A D is bisected by F E

In Figure, A B C is a right triangle right angled at A ,\ B C E D ,\ A C F G\ a n d\ A M N are square on the sides B C ,\ C A\ a n d\ A B respectively. Line segment A X\ _|_D E meets B C at Ydot Show that: a r\ (B Y X D)=2\ a r\ (\ M B C)

A B C D is a parallelogram and E\ a n d\ F are the centroids of triangles A B D\ a n d\ B C D respectively, then E F= (a) A E (b) B E (c) C E (d) D E