Question

determine the relationship between the two triangles and whether or not they can be proven to be congruent.

the two triangles are related by , so the triangles .

Explanation:

Step1: Analyze Triangle Properties

Both triangles are right - angled (one right angle each) and have two sides marked as equal (indicating two congruent sides). Also, the triangles can be related by a rotation (a transformation that preserves shape and size).

Step2: Determine Congruence

For right - angled triangles, if we consider the Hypotenuse - Leg (HL) congruence criterion or the Side - Angle - Side (SAS) criterion. Since both are right triangles, have a right angle, and two sides (the legs or one leg and hypotenuse) are congruent (from the markings), and they are related by rotation (a rigid transformation), rigid transformations preserve congruence. So the triangles are congruent.

Answer:

The two triangles are related by a rotation (a rigid transformation), so the triangles are congruent.