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. 4.145, 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. 6.41, if A B|| D E , /_B A C=35^@ and /_C D E=53^@, find /_D C E .

In Fig. 6.41, if A B|| D E , /_B A C=35^@ and /_C D E=53^@, find /_D C E .

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

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

In Figure, A C=A E ,\ A B=A D\ a n d\ /_B A D=/_E A Cdot Prove that B C=D E

In Fig. 7.21, A C\ =\ A E , A B\ =\ A D and /_B A D\ =/_E A C . Show that B C\ =\ D E .

If D and E are points on sides A B and A C respectively of a triangle A B C such that D E || B C and B D=C E . Prove that A B C is isosceles.

In Figure, B D and C E are two altitudes of a A B C such that B D=C Edot Prove that A B C is isosceles. Figure