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?

• A. Yes, because two angles and the included side ($ASA$) are congruent in both triangles.
• B. Yes, because the $Law$ of $Sines$ shows all corresponding sides are equal.
• C. No, because the triangles could have different side lengths.
• D. No, because the $Law$ of $Sines$ only guarantees similarity, not congruence.

Answer: (A)

Verified step by step guidance

1. Identify the given information for both triangles: angles A = 40\degree, B = 60\degree, and side a = 8 units opposite angle A.
2. Calculate the third angle C in each triangle using the angle sum property of triangles: \(C = 180\degree - A - B\).
3. Recognize that both triangles have two angles and the included side (side a between angles B and C) equal, which corresponds to the ASA (Angle-Side-Angle) congruence criterion.
4. Understand that ASA congruence states if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.
5. Conclude that the triangles are congruent because they satisfy the ASA criterion, meaning all corresponding sides and angles are equal.