In Fig. 5.10, if `A C=B D`, then prove that `A B=C D`.

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

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 .

In fig., if A D_|_B C , prove that A B^2+C D^2=B D^2+A C^2 .

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

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

In Fig. 4.126, (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)

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

In Fig. 4.101, A D and C E are two altitudes of A B C . Prove that A E F ~ C D F (ii) A B D ~ C B E

In Fig. 4.101, A D and C E are two altitudes of A B C . Prove that A E F ~ C D F (ii) A B D ~ C B E (iii) A E F ~ A D B (iv) F D C ~ B E C (FIGURE)