$$In the context of the Law of Sines $\mathrm{Law} \mathrm{of} \mathrm{Sines}$ and triangle geometry, if two lines (such as transversals or sides) are not parallel, which types of angles remain congruent?

Given the Law of Sines, could $a$ and $b$ be the side lengths of a triangle if $a=3$ and $b=7$ and the angle opposite $a$ is $80°$ and the angle opposite $b$ is $40°$?

Which of the following statements is true for triangle $LNM$ according to the Law of Sines?

Which of the following statements correctly describes the requirement for two triangles to be proven similar by the $SAS$ (Side-Angle-Side) similarity theorem?

Given triangle $ABC$ with angles $A$, $B$, and $C$, and corresponding opposite sides $a$, $b$, and $c$, which of the following sets of side lengths could represent a triangle according to the Law of Sines?

Given that line zx bisects angle $\angle wzy$ in triangle wzy, and the measure of angle $\angle yxz$ is $6m-12$ degrees, which of the following could be the value of $m$ if angle $\angle yxz$ is an acute angle?

Given two triangles where in the first triangle, $A$ = $40°$, $B$ = $60°$, and side $a$ = $8$, and in the second triangle, $A$ = $40°$, $B$ = $60°$, and side $a$ = $8$, are the triangles congruent? If so, why?

Given triangle ABC with angles $A$, $B$, and $C$, and corresponding opposite sides $a$, $b$, and $c$, which of the following sets of side lengths could represent a possible triangle according to the Law of Sines?

Which of the following must be true for two triangles to be congruent by the $SSS$ (Side-Side-Side) criterion?