Point `E\ a n d\ F` lie on diagonals `A C` of a parallelogram `A B C D` such that `A E=C Fdot` What type of quadrilateral is `B F D E ?`

A B C D is a trapezium with parallel sides A B=a\ a n d\ D C=bdot If E\ a n d\ F are mid-points of non-parallel sides A D\ a n d\ B C respectively, then the ratio of areas of quadrilaterals A B F E\ a n d\ E F C D is: a : b (b) (a+3b):(3a+b) (3a+b):(a+3b) (d) (3a+b):(3a+b)

A B C D is a parallelogram. If A B is produced to E such that B E=A B . Prove that E D bisects B C .

E , F , G , H are respectively, the mid-points of the sides A B ,B C ,C D and D A of parallelogram A B C D . Show that the quadrilateral E F G H is a parallelogram and that its area is half the area of the parallelogram, A B C Ddot GIVEN : A quadrilateral A B C D in which L ,F ,G ,H are respectively the mid-points of the sides A B ,B C ,C D and D Adot TO PROVE : (i) Quadrilateral E F G H is a parallelogram a r(||^(gm)E F G H)=1/2a r(||^(gm)A B C D) CONSTRUCTION : Join A C and H F

E , F , G , H are respectively, the mid-points of the sides A B ,B C ,C D and D A of parallelogram A B C D . Show that the quadrilateral E F G H is a parallelogram and that its area is half the area of the parallelogram, A B C Ddot

The diagonal B D of a parallelogram A B C D intersects the segment A E at the point F , where E is any point on the side B C . Prove that D F*E F=F B*F Adot

The sides A B\ a n d\ C D of a parallelogram A B C D are bisected at E\ a n d\ F . Prove that E B F D is a parallelogram.

The sides A B and C D of a parallelogram A B C D are bisected at Ea n dF . Prove that E B F D is a parallelogram.

If E ,\ F ,\ G\ a n d\ H are respectively the mid-points of the sides of a parallelogram A B C D ,\ Show that a r(E F G H)=1/2a r\ (A B C D)

E , F , G , H are respectively, the mid-points of the sides of parallelogram A B C D . Show that the area of EFGH is half the area of the parallelogram, A B C Ddot GIVEN : A quadrilateral A B C D in which L ,F ,G ,H are respectively the mid-points of the sides A B ,B C ,C D and D Adot TO PROVE : a r(^(gm)E F G H)=1/2a r(^(gm)A B C D) CONSTRUCTION : Join H and F

In Figure, B D E F\ a n d\ D C E F are each a parallelogram. Is it true that B D=D C ? Why or why not?