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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

Answer :

calculista
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.
${teks-lihat-gambar} calculista
MrRoyal

Similar triangles, may or may not be congruent.

The triangles are congruent by ASA

The given parameters are:

[tex]\mathbf{\triangle RST}[/tex]

[tex]\mathbf{\angle R = 60}[/tex]

[tex]\mathbf{\angle S = 80}[/tex]

[tex]\mathbf{RS = 4}[/tex]

[tex]\mathbf{\triangle EFD}[/tex]

[tex]\mathbf{\angle F = 60}[/tex]

[tex]\mathbf{\angle D = 40}[/tex]

[tex]\mathbf{EF = 4}[/tex]

The third angles of both triangles are:

[tex]\mathbf{\angle T = 180 - 60 - 80}[/tex]

[tex]\mathbf{\angle T = 40}[/tex]

[tex]\mathbf{\angle E = 180 - 60 -40}[/tex]

[tex]\mathbf{\angle E = 100}[/tex]

The above highlights mean that:

  • The triangles have two congruent angles
  • The triangles have one congruent side

This means that, the triangles are congruent by ASA

And the congruent sides are:

[tex]\mathb{RS = EF}[/tex]

Read more about congruent triangles at:

https://brainly.com/question/18799165

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