Georgia is justifying the SSS triangle congruence criteria using △ABC and △LMN (image 1). She transforms the first triangle with a translation to create △A′B′C′ (image 2), followed by a rotation to create △A"B"C" (image 3). She is surprised to see that △A"B"C" overlaps △LMN without having done a reflection. What happened?

Question

Georgia is justifying the SSS triangle congruence criteria using  △ABC  and  △LMN  (image 1). She transforms the first triangle with a translation to create  △A′B′C′  (image 2), followed by a rotation to create  △A"B"C"  (image 3). She is surprised to see that  △A"B"C"  overlaps  △LMN  without having done a reflection. What happened?

(1 point)
Responses

Georgia has shown that the two triangles are congruent. Sometimes three transformations are not necessary when mapping one triangle onto another triangle. 
Georgia has shown that the two triangles are congruent. Sometimes three transformations are not necessary when mapping one triangle onto another triangle.

Georgia has shown that the two triangles are not congruent. If the sequence of transformations does not include a translation, rotation, and reflection, then the triangles cannot be congruent. 
Georgia has shown that the two triangles are not congruent. If the sequence of transformations does not include a translation, rotation, and reflection, then the triangles cannot be congruent.

Georgia made a mistake. She should have done a reflection before the rotation so that her sequence of transformations included all three types of transformations. 
Georgia made a mistake. She should have done a reflection before the rotation so that her sequence of transformations included all three types of transformations.

Georgia made a mistake. She should have translated △ABC along the vector that takes point B to point N, then done a reflection, then done a rotation.
Georgia made a mistake. She should have translated  triangle upper A upper B upper C  along the vector that takes point  upper B to point upper N , then done a reflection, then done a rotation.

GPT-4o mini · Answer

Georgia has shown that the two triangles are congruent. Sometimes three transformations are not necessary when mapping one triangle onto another triangle.

The reasoning here is that congruence can be established through different combinations of transformations, and it is not always necessary to perform all three types (translation, rotation, reflection) to demonstrate that two triangles are congruent. In this case, the translation followed by the rotation was sufficient to show that triangles △ABC and △LMN are congruent.