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 Relationship

One triangle can be obtained from the other by a rotation (or reflection/translation, but rotation is likely here). Check congruence criteria: both have a right angle (marked), a marked equal side, and the included angle? Wait, no—wait, the triangles: one has a right angle, a marked side, and angles. Wait, actually, looking at the markings: each triangle has a right angle, a marked side (equal), and the other angles? Wait, no—wait, the transformation: rotation. Now, for congruence: let's see, in triangle congruence, AAS, ASA, SAS, SSS, HL. Here, if we rotate one triangle, we can see that they have two angles (right angle and another angle) and a side. Wait, actually, the two triangles: one is a rotation of the other. So the relationship is rotation (a rigid transformation, which preserves congruence). So the triangles are congruent because rigid transformations (like rotation) preserve congruence, and also we can use AAS or ASA: right angle, a side, and another angle.

Step2: Determine Congruence

Since rotation is a rigid transformation, the triangles are congruent. So the first blank: rotation (or a rigid transformation), the second: are congruent.

Answer:

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