In ` A B C` (Fig. 4.59), if `/_1=/_2` , prove that `(A B)/(A C)=(B D)/(D C)` . (FIGURE)

In /_\ A B C (Figure), if /_1=/_2 , prove that (A B)/(A C)=(B D)/(D C) .

In Fig. 4.97, if /_A=/_C , then prove that A O B ~ C O 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. 4.125, F E C~= G B D and /_1=/_2 . Prove that A D E A B C . (FIGURE)

In figure /_A C B=90^@ and C D_|_A B . Prove that (B C^2)/(A C^2)=(B D)/(A D) .

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

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

In Fig. 4.179, A B C and D B C are on the same base B C . If A D and B C intersect at O , prove that (A r e a\ ( A B C))/(A r e a\ ( D B C))=(A O)/(D O) (FIGURE)

In Fig. 4.58, A B C is a triangle such that (A B)/(A C)=(B D)/(D C),\ \ /_B=70o,\ \ /_C=50o . Find /_B A D . (FIGURE)