7. Non-Right Triangles

Which of the following sets of angles can be used to construct a triangle?

To prove that two triangles are similar by the SAS similarity theorem, it needs to be shown that two pairs of corresponding sides are in proportion and the included angles are equal. Which of the following statements correctly expresses this condition?

In triangle $ABC$, the measure of angle $A$ is $58°$, and side $a$ is equal to side $c$. What is the measure of angle $C$?

Which of the following statements is true about using the $\mathrm{Law} \mathrm{of} \mathrm{Sines}$ to solve a triangle when given all three side lengths?

Given two parallel lines cut by a transversal, if one of the alternate interior angles measures $m_1=61.8°$, what is the measure of the corresponding alternate interior angle?

In triangle $ABC$, angle $A$ is $30°$, angle $B$ is $45°$, and side $a$ (opposite angle $A$) is $10$ units. Using the Law of Sines, what is the approximate value of side $b$ (opposite angle $B$)?

Given a triangle with vertices $A$, $B$, and $C$, and point $D$ inside the triangle, which of the following must be true for point $D$ to be the orthocenter of the triangle?

Given a circle with points $O$, $A$, and $C$ on its circumference, and major arc $AB$ measures $220°$, what is the measure of angle $\angle OAC$?

In any triangle, which relationship must be true according to the $\mathrm{Law} \mathrm{of} \mathrm{Sines}$?

Which equation can be solved to find one of the missing side lengths in a triangle using the $Law of Sines$?

When using the Law of Sines to solve a triangle, which of the following equations is correct?

In triangle $GHJ$, if $g$ (opposite angle $G$) is $5$ units, $h$ (opposite angle $H$) is $10$ units, and angle $G$ is $30$ degrees while angle $H$ is $60$ degrees, what is the length of line segment $hj$?

Given triangle $FGE$ with sides $f$, $g$, and $e$ opposite angles $F$, $G$, and $E$ respectively, which equation can be used to find the measure of angle $FGE$ using the Law of Sines?

Given two angle measures and the length of the included side in a triangle, how many distinct triangles can be formed?