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

In Figure D E A C and D C a pdot Prove that (B E)/(E C)=(B C)/(C P)

In Figure, /_A C B=90dot and C D_|_A B . Prove that (C B^2)/(C A^2)=(B D)/(A D)

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

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

In /_\ A B C , if A D_|_B C and A D^2=B DxxD C , prove that /_B A C=90dot .

D is a point on the side B C of A B C such that /_A D C=/_B A C . Prove that (C A)/(C D)=(C B)/(C A) or, C A^2=C BxxC D .

In Figure, A E bisects /_C A D\ a n d\ /_B=/_Cdot Prove that A E||B C

In Figure, D E || A C and D F || A E . Prove that (E F)/(B F)=(E C)/(B 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 .