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
, so the triangles
.

Explanation:

Step1: Analyze Triangle Relationships

First, identify the transformation. The second triangle looks like a rotation (and maybe reflection) of the first. Rotation is a rigid transformation (preserves side lengths and angles).

Step2: Congruence via Rigid Transformations

Rigid transformations (rotation, reflection, translation) map a figure to a congruent figure. So if one triangle is a rotation (and reflection) of the other, they have the same side lengths and angles.
For the congruence criteria, we can check: both have two marked equal sides (so two sides) and the included angle (the angle between the two marked sides) looks equal (from the diagram’s angle marking). So by SAS (Side - Angle - Side) congruence, or via rigid transformation, they are congruent.

Answer:

The two triangles are related by rotation (and reflection), so the triangles can be proven congruent (by SAS or rigid transformation).

(For the blanks: First blank: "rotation (and reflection)" (or "a rigid transformation"); Second blank: "can be proven to be congruent")