In Fig. 4.95, if `/_A D E=/_B` show that ` A D E ~ A B C` . If `A D=3. 8 c m` , `A E=3. 6 c m` , `B E=2. 1 c m` and `B C=4. 2 c m` , find `D E` . (FIGURE)

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 Fig. 4.57, A E is the bisector of the exterior /_C A D meeting B C produced in E . If A B=10 c m , A C=6c m and B C=12 c m , find C E . (FIGURE)

In Fig. 9.15, ABCD is a parallelogram, A E_|_D C and C F_|_A D . If A B" "=" "16" "c m , A E" "=" "8" "c m and C F" "=" "10" "c m , find AD.

In Fig. 4.144, we have A B C D E F . If A B=6c m , C D=x\ c m , E F=10 c m , B D=4c m and D E=y\ c m , calculate the values of x and y . (FIGURE)

In Fig. 71, if A B C D\ a n d\ C D E F ,\ find \ /_A C 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=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 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

In Fig. 6.41, if A B|| D E , /_B A C=35^@ and /_C D E=53^@, find /_D 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 Figure, A B C D is a parallelogram, A E _|_D C a n d CC F_|_A D . If A B=16 C M , A E=8c m a n d C F=10 c m , find A D