7. Non-Right Triangles

Which of the following criteria always proves triangles congruent when using the $\mathrm{Law} \mathrm{of} \mathrm{Sines}$?

Given three segments with lengths $a$, $b$, and $c$, which of the following sets of values could form a triangle according to the Law of Sines and the triangle inequality?

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?

In triangle $ABC$, side $a$ is $11$ ft and side $b$ is $13$ ft. Which of the following could be the length of side $c$ if angle $C$ is opposite side $c$ and angle $C$ is the largest angle in the triangle?

Given that the triangles in the diagram are congruent and $mF$ = $40°$, what is the measure of angle $G$ in the congruent triangle?

Classify the triangle, then solve: $A=60°,B=15°,c=6$.

The bearing of a lighthouse from a ship was found to be N 37° E. After the ship sailed 2.5 mi due south, the new bearing was N 25° E. Find the distance between the ship and the lighthouse at each location.

Which statement regarding the interior and exterior angles of a triangle is always true?

Given triangle $△abc$, which triangle is congruent to $△abc$ by the ASA (Angle-Side-Angle) criterion?

Given triangle $△efg$, which equation could be used to find the measure of angle $e$ using the Law of Sines?

Which of the following pairs of triangles can be proven congruent using the $\mathrm{SAS}$ (Side-Angle-Side) criterion rather than the Law of Sines?

Given two triangles $△wxz$ and $△yzx$, which congruence theorem can be used to prove that they are congruent?

Given that $m\angle 1=m\angle 4$, $m\angle 2=m\angle 3$, $m\angle 1+m\angle 4=180°$, and $m\angle 2+m\angle 3=180°$, which of the following best describes the relationship between the angles in two triangles that allows the Law of Sines to be applied?

Given a triangle with side lengths $10$ in., $10$ in., and $10$ in., which classification best represents this triangle?

Which of the following lists of angle measures could be the angle measures of a triangle?