Question

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

Answer 1

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
Angles RS and Angles EF are equals

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.