If ` A B C\ a n d\ D E F` are two triangles such that `A B ,\ B C` are respectively equal and parallel to `D E ,\ E F ,` then show that Quadrilateral `A B E D` is a parallelogram Quadrilateral `B C F E` is a parallelogram `A C=D F` (iv) ` A B C\ ~=\ D E F`

In DeltaA B C and DeltaD E F , A B\ =\ D E , A B\ ||\ D E , B C\ =\ E F and B C\ ||\ E F . Vertices A, B and C are joined to vertices D, E and F respectively (see Fig. 8.22).Show that (i) quadrilateral ABED is a parallelogram (ii) quadrilateral BEFC is a parallelogram (iii) AD || CF and AD = CF (iv) quadrilateral ACFD is a parallelogram (v) AC = DF (vi) ∆ ABC ≅ ∆ DEF.

In Figure A B C D\ a n d\ A E F D are two parallelograms. Prove that: P E=F Q

In Fig. 71, if A B C D\ a n d\ C D E F ,\ find \ /_A C E

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

Identify A, B, C, D, E, F,G

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

In Figure, A B C\ a n d\ B D E are two equilateral triangls such that D is the mid-point of B CdotA E intersects B C in Fdot Prove that: a r\ (\ B F E)=\ 2\ a r\ (E F D)

In a A B C ,\ E\ a n d\ F are the mid-points of A C\ a n d\ A B respectively. The altitude A P\ to\ B C intersects F E\ at Qdot Prove that A Q=Q P

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

In Figure, A B C D is a parallelogram and E F C D is a rectangle. Also A L _|_D Cdot Prove that a r(A B C D=a r(E F C D) a r (a A B C D)=D C x A L