Mario is trying to prove the SSS congruency theorem using the triangles pictured in image 1 below. He translated △ABC

Question

to create △A′B′C′
as shown in image 2 and then performed a rotation to create △A"B"C"
as shown in image 3. Surprisingly, he found that △A"B"C"
overlapped △LMN
without him having to do a reflection. What happened?

(1 point)
Responses which answer is correct and why

Mario made a mistake. He should have translated △ABC
so that point B moved to point N, then done a reflection, then a rotation
Mario made a mistake. He should have translated △ABC
so that point B moved to point N, then done a reflection, then a rotation

Mario has shown that the two triangles are not congruent because if the sequence of transformations is not a translation, a rotation and then a reflection, then there is no way that the triangles can be congruent.
Mario has shown that the two triangles are not congruent because if the sequence of transformations is not a translation, a rotation and then a reflection, then there is no way that the triangles can be congruent.

Mario made a mistake. He should have completed a reflection before the rotation so that there were three transformations in the sequence, 1 of all three types.
Mario made a mistake. He should have completed a reflection before the rotation so that there were three transformations in the sequence, 1 of all three types.

Mario has shown that the trwo triangles are congruent. Three transformations are not always necessary when moving 1 triangle on top of the other.
Mario has shown that the trwo triangles are congruent. Three transformations are not always necessary when moving 1 triangle on top of the other.
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Answer 1

The correct response is:

Mario has shown that the two triangles are congruent. Three transformations are not always necessary when moving 1 triangle on top of the other.

This is because congruency can be established through any sequence of transformations that result in one triangle overlapping the other. While the SSS (Side-Side-Side) congruency theorem states that if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent, the specific nature of transformations (translation, rotation, reflection) is not a requirement for showing congruency. In this case, Mario successfully positioned triangle A"B"C" over triangle LMN without needing to perform a reflection, which still validates the congruency of the two triangles. Therefore, the idea that transformations have to include one of each type (translation, rotation, reflection) is not accurate in proving congruence.