Georgia is justify the SSS triangle congruence criteria using triangle ABC and triangle LMN. she transforms the first triangle with a translation to create triangle A'B'C', followed by a rotation to create triangle A"B"C" overlaps triangle LMN without having done a reflection. what happened?

Question

A. Georgia has shown that two triangle are not congruent. if the sequence of transformations does not include a translation, rotation, and reflection, then the triangles cannot be congruent
B. 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.
C. Georgia made a mistake. she should have translated triangle ABC along the vector that takes point B to point N, then done a reflection, then done a rotation
D. georgia has shown that the two triangles are congruent. sometimes three transformations are not necessary when mapping one triangle onto another triangle

Answer 1

The correct answer is:

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

In geometry, two triangles can be shown to be congruent through a combination of transformations (translations, rotations, and reflections). If Georgia was able to transform triangle ABC into triangle LMN using only a translation and a rotation without any reflection, it indicates that the two triangles are congruent. It is not always necessary to use all three types of transformations; sometimes, just a combination of two transformations can suffice to demonstrate congruence.