Question

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:

Step1: Analyze reflection property

Reflections are rigid transformations. Rigid transformations produce congruent images. So, the statement "Reflections produce an image that is congruent to the pre - image" is true.

Step2: Analyze transitive property of congruence

The transitive property of congruence states that if \(A\cong B\) and \(B\cong C\), then \(A\cong C\). In the context of transformations, if a first transformation maps a pre - image to an image (say \(I_1\)) and a second transformation maps \(I_1\) to a final image \(I_2\), and both transformations are congruence transformations (like reflection, rotation, translation), then the pre - image is congruent to the final image. So, "The transitive property of congruence says that the final image is congruent to the pre - image" is true.

Step3: Analyze rotation property

Rotations are also rigid transformations. Rigid transformations preserve shape and size, which means they produce congruent images. So, the statement "Rotations do not produce an image that is congruent to the pre - image" is false.

Step4: Analyze translation property

Translations are rigid transformations. A translation of a pre - image results in an image that has the same shape and size as the pre - image. So, the statement "If the image can be shown to be the result of one of a translation, then the image is congruent to its pre - image" is true.

Answer:

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