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: Analyze Triangle Sides

Each triangle has two sides with markings: one side with two ticks (equal) and one with one tick (equal), and they share a common angle (the included angle between the marked sides).

Step2: Apply SAS Congruence

By the Side - Angle - Side (SAS) congruence criterion, if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent. Here, the two triangles have two pairs of equal sides (marked) and the included angle is common (or equal due to the way the triangles are related, likely a reflection or rotation which preserves angle and side lengths), so they are related by a transformation (like reflection) that preserves congruence, and by SAS, they are congruent.

Answer:

The two triangles are related by a reflection (or other congruence - preserving transformation), so the triangles can be proven to be congruent (by SAS congruence criterion). The first blank can be filled with a description of the transformation (e.g., reflection) or directly state the congruence relation setup, and the second blank is "can be proven to be congruent". If we follow the typical answer for such triangle congruence with two sides and included angle: The two triangles are related by a congruence - preserving transformation (e.g., reflection), so the triangles can be proven to be congruent (using SAS).