Question

determine the relationship between the two triangles and whether or not they can be proven to be congruent.
answer attempt 1 out of 2
the two triangles are related by , so the triangles

Explanation:

Step1: Identify Given Information

Both triangles have a pair of equal sides (marked with ticks) and a pair of equal angles (marked with the same arc). Also, we can check the transformation: one triangle can be rotated (and maybe reflected) to align with the other.

Step2: Analyze Congruence Criterion

The triangles have two sides and the included angle? Wait, no—wait, looking at the markings: one triangle has a side, included angle, and another side? Wait, actually, the triangles can be related by a rotation (and possibly reflection). Let's check the congruence: the triangles have two sides equal (the ticked sides) and the included angle equal (the arc - marked angle). Wait, no, maybe SAS? Wait, actually, when we rotate one triangle, we can see that the corresponding sides and angles match. So the relationship is a rotation (and maybe reflection), and the congruence: since two sides and the included angle? Wait, no, let's re - examine. The triangles: one has a side, angle, side? Wait, the key is that the triangles can be mapped to each other via a rotation (and reflection), so they are related by rotation (and reflection), and by the SAS (Side - Angle - Side) congruence criterion? Wait, no, actually, when you rotate a triangle, it's congruent. So the two triangles are related by rotation (and reflection), so the triangles are congruent by SAS (if the sides and included angle match) or by the fact that rotation is a congruence transformation.

Wait, let's correct: The triangles have two sides with the same tick marks (so equal length) and the included angle (the angle between the two sides) is equal (marked with the same arc). So by the SAS (Side - Angle - Side) congruence postulate, the triangles are congruent. And the relationship between them is a rotation (and possibly a reflection) to map one onto the other.

Answer:

The two triangles are related by rotation (and reflection), so the triangles are congruent by SAS (or by the congruence of rotated figures).