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 a b c or d

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 answer is:

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

Explanation:

Mario successfully translated and rotated triangle \( \triangle ABC \) to coincide with triangle \( \triangle LMN \), demonstrating that \( \triangle ABC \) and \( \triangle LMN \) are congruent. Congruence can be established through various sequences of transformations, and it is not strictly necessary to have one of each type (translation, rotation, reflection) to prove congruence. In this case, the translation followed by the rotation was sufficient to show that the two triangles overlapped exactly, indicating they are indeed congruent.