Question

determine the relationship between the two triangles and whether or not they can be proven to be congruent.
answer attempt 2 out of 2
the two triangles are related by side-angle-side (sas), so the triangles can be proven congruent

Explanation:

Step1: Identify Given Information

Each triangle has one marked (congruent) side and one marked (congruent) angle. The included angle and side relationship? Wait, looking at the triangles: one triangle has a side, an included angle, and the other triangle has the same - side marked, angle marked, and the other side? Wait, SAS congruence: two sides and the included angle. Wait, in the two triangles, we see one side is marked (congruent), one angle is marked (congruent), and the other side? Wait, no, let's check the markings. Each triangle has one side with a tick (so congruent sides) and one angle with a curve (congruent angles). Also, the angle is between the marked side and another side? Wait, actually, in SAS, if two sides and the included angle are congruent, then triangles are congruent. Here, the two triangles have a congruent side (marked), a congruent included angle (marked), and the other side? Wait, no, maybe the orientation. Wait, the key is: the two triangles have a pair of congruent sides (marked), a pair of congruent included angles (marked), and the other pair of sides? Wait, no, in SAS, it's two sides and the included angle. So if we have one side congruent, the included angle congruent, and the other side congruent? Wait, maybe the triangles are related by SAS: one side (marked), included angle (marked), and the other side? Wait, maybe the diagram shows that the two triangles have a congruent side, a congruent included angle, and the other side (from the angle) is also congruent? Wait, the initial answer says SAS, so let's verify.

Step2: Apply SAS Congruence Criterion

The SAS (Side - Angle - Side) congruence postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. In the given triangles, we have one pair of congruent sides (marked with the same tick), one pair of congruent included angles (marked with the same curve), and the other pair of sides (adjacent to the angle) – wait, no, actually, in the diagram, each triangle has a side with a tick, an angle with a curve, and the other side (from the angle) which, due to the angle being included, if the side and angle are congruent, and the other side (from the angle) is also congruent? Wait, maybe the triangles are oriented differently, but the markings show that one side is congruent, the included angle is congruent, and the other side (forming the angle) is congruent. So by SAS, they are congruent.

Answer:

The two triangles are related by Side - Angle - Side (SAS), so the triangles can be proven congruent.