Question

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 Properties

Both triangles are right - angled (have a right angle). Let's check the side markings. One triangle has two sides with markings (one double, one single) and the other also has two sides with markings (one double, one single). A rotation (like a 90 - degree rotation or other rotational transformation) can map one triangle to the other. For congruence, we can use the Hypotenuse - Leg (HL) theorem or Side - Angle - Side (SAS) theorem. Since they are right - angled, and we have two sides (the legs or one leg and hypotenuse) marked as equal, the triangles are related by rotation, and we can prove them congruent.

Step2: Determine Relationship and Congruence

The two triangles are related by a rotation (a type of rigid transformation). For congruence, in right - angled triangles, if we consider the marked sides, by SAS (since we have a right angle, and two sides around the right angle or one leg and hypotenuse) or HL, the triangles can be proven congruent.

Answer:

The two triangles are related by \(\boldsymbol{\text{rotation}}\), so the triangles \(\boldsymbol{\text{can be proven to be congruent}}\).