In Fig. 4.141 `D E B C` such that `A E=(1//4)A C` . If `A B=6c m` , find `A D` . (FIGURE)

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)

In Fig. 4.143, /_A=/_C E D , prove that C A B∼ C E D . Also, find the value of x . (FIGURE)

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 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. 4.42, A D is the bisector of /_B A C . If A B=10 c m . A C=14 c m and B C=6c m , find B D and D C . (FIGURE)

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 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. 4.57, 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. 4.41, A D is the bisector of /_A . If B D=4c m , D C=3c m and A B=6c m , determine A C . (FIGURE)

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