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, A B_|_B C ,F G_|_B C and D E_|_AC.Prove that triangle A D E~G C F

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

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. 4.128, D E F G is a square and /_B A C=90o . Prove that A G F D B G (ii) A G F E F C (FIGURE) (iii) D B G E F C (iv) D E^2=B DxxE C

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

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

In A B C , if B D_|_A C and B C^2=2\ A C C D , then prove that A B=A C .