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
2 answers:
The
correct answer is in file attached
<span>we have<span>
</span>triangle RST<span>
</span><span>m∠R = 60, m∠S = 80 and m∠T=180-(80+60)=40</span></span>
<span>RS=4<span>
</span>triangle EFD<span>
</span><span>m∠F = 60, m∠D = 40 and m∠E=180-(60+40)=80</span></span>
EF=4
Therefore
<span>The triangles RST<span> and </span>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).</span>
Explication
Side common--------> RS=EF
<span>Angles RS------------- > m∠<span>R = 60 m</span>∠S = 80 </span>
<span>Angles EF------------- > m∠<span>E = 80 m</span>∠F = 60 </span>
<span>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.</span>
<span>we have<span>
</span>triangle RST<span>
</span><span>m∠R = 60, m∠S = 80 and m∠T=180-(80+60)=40</span></span>
<span>RS=4<span>
</span>triangle EFD<span>
</span><span>m∠F = 60, m∠D = 40 and m∠E=180-(60+40)=80</span></span>
EF=4
Therefore
<span>The triangles RST<span> and </span>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).</span>
Explication
Side common--------> RS=EF
<span>Angles RS------------- > m∠<span>R = 60 m</span>∠S = 80 </span>
<span>Angles EF------------- > m∠<span>E = 80 m</span>∠F = 60 </span>
<span>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.</span>
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