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

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 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 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.

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.

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.

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. Mario's process of translating and then rotating the triangle allows him to align the triangles without the need for a reflection, which demonstrates that they can still be congruent.