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
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Explanation:

Step1: Analyze Triangle Properties

Both triangles are right - angled (one angle is \(90^{\circ}\)). They have two pairs of congruent sides (marked with the same tick marks) and the included right angle. By the Side - Angle - Side (SAS) congruence criterion, if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent. Also, the triangles are related by a reflection (a transformation that flips the triangle over a line, which preserves side lengths and angles).

Step2: Determine Congruence

Since we can identify the congruent parts (two sides and the included right angle) using the markings and the right - angle property, and the transformation (reflection) also preserves the congruence of the triangles, we can conclude the congruence.

Answer:

The two triangles are related by reflection, so the triangles are congruent (by SAS congruence criterion, as they have two congruent sides and the included right angle).