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`

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

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 DdotE 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

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)dot Show that DE ll BC .

X Y isa line parallel to side B C of A B CdotB E A 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)dot

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

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 .

X Y is a line parallel to side B C of triangle A B C. BE ll AC and CF ll AB meet XY in E and F respectively. Show that a r( A B E)=a r( A C F)dot

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