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` .

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 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=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=8x-7, D B=5x-3, A E=4x-3 and E C=(3x-1) , find the value of x . (ii) If A D=4x-3, A E=8x-7, B D=3x-1 and C E=5x-3 , find the volume x . (iii) If A D=2. 5 c m , B D=3. 0 c m and A E=3. 75 c m , find the length of 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 .

In a A B C , D and E are points on A B and A C respectively such that D E// B C . If A D=2. 4 c m ,\ \ A E=3. 2 c m ,\ \ D E=2c m and B C=5c m , find B D and C E .

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=10. 8 c m ,\ \ B D=4. 5\ c m ,\ \ A C=4. 8 c m\ a n d\ A E=2. 8 c m (ii) A D=5. 7 c m ,\ \ B D=9. 5 c m ,\ \ A E=3. 3 c m\ a n d\ E C=5. 5 c m .

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

A B C D is a square E ,\ F ,\ G\ a n d\ H are points on A B ,\ B C ,\ C D\ a n d\ D A respectively, such that A E=B F=C G=D Hdot Prove that E F G H is square.