Multiple Choice
Which of the following pairs of triangles can be proven congruent using the ?
7. Non-Right Triangles
Law of Sines
Multiple Choice
According to the , which set of angle measures could represent the angles of a triangle?
A
, ,
B
, ,
C
, ,
D
, ,
Verified step by step guidance1
Recall that the sum of the interior angles of any triangle must be exactly \(180^\circ\). This is a fundamental property of triangles.
Check each given set of angles to see if their sum equals \(180^\circ\). For example, for the set \(120^\circ\), \(30^\circ\), and \(40^\circ\), calculate \$120 + 30 + 40$.
Eliminate any sets where the sum of the angles is not \(180^\circ\), since such sets cannot represent the angles of a triangle.
Understand that the Law of Sines states that for a triangle with angles \(A\), \(B\), and \(C\) and opposite sides \(a\), \(b\), and \(c\), the ratio \(\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}\) holds true, but this only applies if the angles form a valid triangle.
Confirm that the remaining sets of angles not only sum to \(180^\circ\) but also can satisfy the Law of Sines, which is always true for valid triangles, so the key step is verifying the angle sum.
Related Videos
Related Practice
