Question

5
sarah claims that any pair of equilateral triangles can be proven to be congruent by satisfying the sss congruence criteria.
select the true statement.
a. sarah is incorrect because there are pairs of equilateral triangles which can be mapped onto each other by a rigid transformation.
b. sarah is correct because no pair of equilateral triangles can be mapped onto each other by a rigid transformation.
c. sarah is correct because every pair of equilateral triangles can be mapped onto each other by a rigid transformation.
d. sarah is incorrect because there are pairs of equilateral triangles which cannot be mapped onto each other by a rigid transformation.

Explanation:

To determine the correct statement, we analyze the properties of equilateral triangles and congruence (via rigid transformations). An equilateral triangle has all sides equal, but two equilateral triangles can have different side lengths. Rigid transformations (translation, rotation, reflection) preserve side lengths. So, if two equilateral triangles have different side lengths, they can't be mapped onto each other by a rigid transformation. Sarah claims any pair can be proven congruent by SSS, but SSS requires all three corresponding sides to be equal. If side lengths differ, SSS isn't satisfied, and they can't be mapped via rigid transformations. So Sarah is incorrect, and option D correctly states there are pairs of equilateral triangles that can't be mapped by rigid transformations.

Answer:

D. Sarah is incorrect because there are pairs of equilateral triangles which cannot be mapped onto each other by a rigid transformation.