MATH SOLVE

2 months ago

Q:
# 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

Accepted Solution

A:

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.

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.