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\ 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 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)=3/4 , then write Area ( 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)=2/5 , then A r e a( A B C): A r e a( D E F)=

In triangle ABC, D and E are mid-points of sides AB and BC respectively. Also, F is a point in side AC so that DF is parallel to BC (i) Prove that DBEF is a parallelogram.

In triangle ABC, angle B is obtuse. D and E are mid-points of sides AB and BC respectively and F is a point on side AC such that EF is parallel to AB. Show that BEFD 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.

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) .

D, E and F are the mid-points of the sides BC, CA and AB, respectively of an equilateral Delta ABC. Show that Delta DEF is also an equilateral triangle.