Question

which statement is not true?
reflections
produce an image
that is congruent to
the pre - image.
the transitive
property of
congruence says
that the final image
is congruent to the
pre - image.
rotations do not
produce an image
that is congruent to
the pre - image.
if the image can be
shown to be the
result of one of a
translation, then
the image is
congruent to its
pre - image.

Explanation:

• Reflections: Reflections are rigid transformations. Rigid transformations preserve the shape and size of a figure. So, reflections produce an image that is congruent to the pre - image.
• Transitive property of congruence: If \(A\cong B\) and \(B\cong C\), then \(A\cong C\). In the context of transformations, if a figure is transformed (e.g., reflected, rotated, translated) multiple times, the final image is congruent to the pre - image.
• Rotations: Rotations are also rigid transformations. Rigid transformations do not change the shape and size of a figure. So, rotations produce an image that is congruent to the pre - image.
• Translations: Translations are rigid transformations. Rigid transformations preserve congruence. So, if the image is the result of a translation, then the image is congruent to its pre - image.

Answer:

The statement “Rotations do not produce an image that is congruent to the pre - image” is not true.