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 `D E B Cdot`

D and E are points on sides AB and AC respectively of DeltaA B C such thata r" "(D B C)" "=" "a r" "(E B C) . Prove that D E" "||" "B C .

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

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 a A B C , D and E are points on the sides A B and A C respectively such that D E B C If A D=6\ c m , D B=9\ c m and A E=8\ c m , find A C . (ii) If (A D)/(D B)=3/4 and A C=15\ c m , find A E . (iii) If (A D)/(D B)=2/3 and A C=18\ c m , find A E .

In a A B C , D and E are points on the sides A B and A C respectively such that D E B C If A D=4 , A E=8 , D B=x-4 , and E C=3x-19 , find x (ii) If A D=8 c m , A B=12 c m and A E=12 c m , find C E . (iii) If A D=4 c m , D B=4. 5 c m and A E=8 c m , find A C .

In a A B C , D and E are points on the sides A B and A C respectively such that D E B C If A D=2 c m , A B=6 c m and A C=9 c m , find A E . (ii) If (A D)/(B D)=4/5 and E C=2. 5 c m , find A E . (iii) If A D=x , D B=x-2 , A E=x+2 and E C=x-1 , find the value of x .

A point D is taken on the side B C of a A B C such that B D=2d Cdot Prove that a r( A B D)=2a r( A D C)dot

In a A B C , D a n d E are points on the sides A B and A C respectively. For each of the following cases show that D E B C : A B=12 c m , A D=8 c m , A E=12 c m a n d A C=18 c m . (ii) A B=5. 6 c m , A D=1. 4 c m , A C=7. 2 c m a n d A E=1. 8 cm

Triangles A B C and +DBC are on the same base B C with A, D on opposite side of line B C , such that a r(_|_ A B C)=a r( D B C)dot Show that B C bisects A Ddot

In Figure D\ a n d\ E are two points on B C such that B D=D E=E Cdot Show that a r(\ A B D)=\ a r\ (\ A D E)=a r\ (\ A E C)dot