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
(i) Quadrilateral `A B E D` is a parallelogram
(ii) Quadrilateral `B C F E` is a parallelogram
(iii) `A C=D F`
(iv) ` A B C\ ~=\ D E F`

If A B C and 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 (i) quad ABED is a parallelogram (ii) quad BCFE is a paralellogram (iii) AC=DF (iv) Delta ABC ~= Delta DEF

If A B C and D E F are similar triangles such that 2\ A B=D E and B C=8c m , then 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.

If A B C and D E F are two triangles such that (A B)/(D E)=(B C)/(E F)=(C A)/(F D)=2/5 , then A r e a( A B C): A r e a( D E F)=

If A B C and D E F are two triangles such that (A B)/(D E)=(B C)/(E F)=(C A)/(F D)=3/4 , then write Area ( A B C): A r e a( D E F) .

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

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.

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

In Figure, A B||C F\ a n d\ B C||E D . Prove that /_A B C=\ /_F D E

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