Ask a New Question
Menu

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

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 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.
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 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.
Skip to navigation

1 answer

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

The SSS (Side-Side-Side) congruence theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. Mario's sequence of transformations (translation and rotation) resulted in overlapping triangles, which demonstrates congruence without the necessity of completing a reflection. Therefore, he has correctly shown congruence through his transformations.