In Fig. 4.133, if ` A B E~= A C D` , prove that ` A D E A B C` . (FIGURE)

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

In Figure, if A B=A C\ a n d\ B E=C D , prove that A D=A Edot

In Fig. 4.125, F E C~= G B D and /_1=/_2 . Prove that A D E A B C . (FIGURE)

In Fig. 4.145, if A B_|_B C , D C_|_B C and D E_|_A C , prove that C E D ∼ A B C . (FIGURE)

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

In Figure, if B D_|_A C and C E_|_A B , prove that (i) /_\A E C ~ /_\A D B (ii) (C A)/(A B)=(C E)/(D B)

In Fig. 4.124, E is a point on side C B produced of an isosceles triangle A B C with A B=A C . If A D_|_B C and E F_|_A C , prove that (i) A B D E C F (ii) A BxxE F=A DxxE C . (FIGURE)

In Fig. 4.31, if (A D)/(D C)=(B E)/(E C) and /_C D E=/_C E D , prove that C A B is isosceles. (FIGURE)

In Fig. 4.126, (O A)/(O C)=(O D)/(O B) . Prove that /_A=/_C and /_B=/_D . (FIGURE)

In Fig. if E F|| D C|| A Bdot Prove that (A E)/(E D)=(B F)/(F C) . (FIGURE)