Which of the following pairs of triangles are congruent by the Angle-Side-Angle (ASA) criterion according to the Law of Sines?

• A. Triangle 1: $A=40°$, $B=70°$, $c=8$; Triangle 2: $A=40°$, $B=70°$, $c=8$
• B. Triangle 1: $A=30°$, $B=80°$, $a=10$; Triangle 2: $A=30°$, $B=70°$, $a=10$
• C. Triangle 1: $A=50°$, $B=60°$, $a=7$; Triangle 2: $A=50°$, $B=60°$, $b=7$
• D.

Answer: (A)

Verified step by step guidance

1. Recall that the Angle-Side-Angle (ASA) criterion for triangle congruence states that if two angles and the included side (the side between those two angles) of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.
2. For each pair of triangles, identify the two given angles and the side length, and check if the side is the one included between the two angles. The included side is the side that lies between the two given angles.
3. In the first pair, both triangles have angles \(A = 40^\circ\) and \(B = 70^\circ\), and side \(c = 8\). Since side \(c\) is opposite angle \(C\), verify if \(c\) is the side between angles \(A\) and \(B\). If yes, this pair satisfies ASA.
4. In the second pair, the triangles have angles \(A = 30^\circ\) and \(B = 80^\circ\) (first triangle) and \(B = 70^\circ\) (second triangle), and side \(a = 10\). Since the angles differ, or the side is not included between the two angles, this pair does not satisfy ASA.
5. In the third pair, both triangles have angles \(A = 50^\circ\) and \(B = 60^\circ\), but the first triangle has side \(a = 7\) and the second has side \(b = 7\). Since the side lengths correspond to different sides, check if these sides are included between the given angles. If not, this pair does not satisfy ASA.