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).`

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) .

Show that the segment joining the mid-points of a pair of opposite sides of a parallelogram, divides it into two equal parallelograms. GIVEN : A parallelogram A B C D,E and F are the mid-points of opposite sides A B and C D respectively. TO PROVE : a r(||^(gm)A E F D)=a r(||^(gm)E B C F) CONSTRCUTION : Join E Fdot

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

In A B C ,\ D and E are points on sides A B and A C respectively such that A DxxE C=A ExxD B . Prove that D E B C .

p\ A N D\ q are any two points lying on the sides D C\ a n d\ A D respectively of a parallelogram A B C Ddot\ Show that a r( A P B)=a r\ ( B Q C)dot

In Figure, D , E are points on sides A B and A C respectively of /_\A B C , such that a r( B C E)=a r( B C D) . Show that DE||BC .

In Figure, D , E are points on sides A B and A C respectively of A B C , such that a r( B C E)=a r( B C D)dot Show that DE ll BC .

In a A B C ,D and E are points on sides A B a n d A C respectively such that B D=C E . If /_B=/_C , show that DE || BC .

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

X Y is a line parallel to side B C of /_\ A B C . B E || AC and C F || A B meet X Y in E and F respectively. Show that a r( A B E)=a r( A C F) .