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

Similar triangles, may or may not be congruent.

The triangles are congruent by ASA

The given parameters are:

The third angles of both triangles are:

The above highlights mean that:

The triangles have two congruent anglesThe triangles have one congruent side

This means that, the triangles are congruent by ASA

And the congruent sides are:

Read more about congruent triangles at:

link

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.