If `D ,E ,F` are the mid-points of the sides `B C ,C Aa n dA B` respectively of a triangle `A B C ,` prove by vector method that `A r e aof D E F=1/4(a r e aof A B C)dot`

D ,\ E ,\ F are the mid-points of the sides B C ,\ C A and A B respectively of a Delta A B C . Determine the ratio of the areas of D E F and A B C .

D ,\ E ,\ F are the mid-points of the sides B C ,\ C A and A B respectively of a A B C . Determine the ratio of the areas of D E F and A B C .

If D ,Ea n dF are three points on the sides B C ,C Aa n dA B , respectively, of a triangle A B C such that the (B D)/(C D),(C E)/(A E),(A F)/(B F)=-1

If D ,E and F are three points on the sides B C ,CA and A B , respectively, of a triangle A B C show that the (B D)/(C D)=(C E)/(A E)=(A F)/(B F)=-1

If D ,Ea n dF are three points on the sides B C ,C Aa n dA B , respectively, of a triangle A B C such that AD,BE and CF are concurrent, then show that (B D)/(C D),(C E)/(A E),(A F)/(B F)=-1

If the vectors vec a , vec b ,a n d vec c form the sides B C ,C Aa n dA B , respectively, of triangle A B C ,t h e n

If the vectors vec a , vec b ,a n d vec c form the sides B C ,C Aa n dA B , respectively, of triangle A B C ,t h e n

D ,\ E ,\ F are the mid-point of the sides B C ,\ C A\ a n d\ A B respectively of /_\ A B C . Then D E F is congruent to triangle. (a)A B C (b) AEF (c) B F D ,\ C D E (d) A F E ,\ B F D ,\ C D E

D ,\ E ,\ F are the mid-point of the sides B C ,\ C A\ a n d\ A B respectively of A B Cdot Then D E F is congruent to triangle. A B C (b) AEF (c) B F D ,\ C D E (d) A F E ,\ B F D ,\ C D E

In Figure, A B C D is a parallelogram. E and F are the mid-points of the sides A B and C D respectively. Prove that the line segments A F and C E triset (divide into three equal parts) the diagonal B Ddot