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, \(90^{\circ}\)). Let's look at the marked sides (congruent side markings). For the first triangle, two sides are marked with one and two tick marks respectively, and for the second triangle, the sides with the same tick marks are present. Also, we can consider the transformation. A rotation (specifically a \(90^{\circ}\) or other rotational transformation) can map one triangle onto the other.

Step2: Determine Congruence

We can use the Hypotenuse - Leg (HL) congruence criterion for right - angled triangles. In right - angled triangles, if the hypotenuse and one leg of one triangle are congruent to the hypotenuse and one leg of another right - angled triangle, then the triangles are congruent. Alternatively, since we can rotate one triangle to match the other (rotation is a rigid transformation that preserves side lengths and angles), the triangles are related by rotation, and since rotation preserves congruence, the triangles are congruent.

Answer:

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