if Given : Line BC is congruent to Line EF
Lines AC Is congruent to Line EGO
Line AC is broken up in Segments AB =10 and BC=3
Line EG is broken up in Segments EF and FG

How do I Prove FG= 10 With reasons??

Question

if Given : Line BC is congruent to Line EF 
                Lines AC Is congruent to Line EGO
Line AC is broken up in  Segments AB =10 and BC=3
Line EG is broken up in Segments EF and FG

How do I Prove FG= 10   With reasons??

phi · Answer

Do you mean
  Lines AC Is congruent to Line EG  (not EGO) ?

EF= BC  reason:  Given (BC congruent to EF)
BC= 3    reason:  given  (length of BC is 3)
EF=  3    reason:  things equal to the same thing are equal to each other

AC= EF   reason:  Given
AC= AB+BC   reason: a whole is the sum of its parts
AC = 10+3 = 13  reason:  given (AB=10 and BC=3)

EG= EF+FG    reason: whole is the sum of its parts
EG= 3 + FG    reason:  EF = 3
EG= AC          reason: given (AG congruent to EG)
EG= 13          reason:  AC=13.  the parts must add up to the whole

13= 3+FG      reason:  13= EG and 3+FG=13  (things = to the same thing are equal to each other

10= FG            reason: