In Figure 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`.

In Figure, if /_\ A B E~= /_\A C D , prove that /_\ A D E ~ /_\ A B C .

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 the figure given below D E || B C . If A D=2. 4 c m , D B=3. 6 c m and A C=5c m , Find A E .

In a /_\ A B C , A D is the bisector of /_A , meeting side B C at D . (i) If B D=2. 5 c m ,\ \ A B=5c m and A C=4. 2 c m , find D C . (ii) If B D=2c m ,\ \ A B=5c m and D C=3c m , find A C . (iii) If A B=3. 5 c m , A C=4. 2 c m and D C=2. 8 c m , find B D .

In Figure, If A B || C D\ a n d\ C D\ || E F , Find /_A C E .

In Fig. if A B_|_B C and D E_|_A C . Prove that A B C ~ A E D

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. 4.140, /_A B C=90o and B D_|_A C . If A B=5. 7 c m , B D=3. 8\ c m and C D=5. 4 c m , find B C . (FIGURE)

In Figure, D E || B C in /_\ A B C such that B C=8c m , A B=6c m and D A=1. 5 c m . Find D E .

In Fig. 4.241, D E B C and A D=1/2B D . If B C=4. 5 c m , find D E . (FIGURE)