R, S, and T are the vertices of one triangle. E, F, and D are the vertices of another triangle. m∠R = 60, m∠S = 80, m∠F = 60, m∠D = 40, . Are the two triangles congruent? If yes, explain and tell which segment is congruent to

The correct answer is in file attached  
we have
triangle RST
m∠R = 60, m∠S = 80  and m∠T=180-(80+60)=40
RS=4
triangle EFD
m∠F = 60, m∠D = 40  and m∠E=180-(60+40)=80
EF=4  
Therefore
  The triangles RST  and EFD are congruents because they have two angles and the side common to them, respectively, equal.
This is the theorem of ASA (angle-side-angle).
Explication
Side common--------> RS=EF
Angles RS------------- > m∠R = 60  m∠S = 80 
Angles EF------------- > m∠E = 80  m∠F = 60     

The segment which is congruent to RT is FD, because angles of RT are 60 and 40, and angles of FD also are 60 and 40.