We are asked to explain how a sequence of translations, reflections, and rotations results in congruent figures. First, let's recall what it means for two figures to be congruent.

Congruent Figures
Two figures are congruent when they have the same shape and size.

Now, recall what we know about translations, reflections, and rotations. We will focus on whether or not each of these transformations affects the shape or size of a figure.

Translation	A translation slides a figure around without turning it. It does not affect the shape or size of the figure.
Reflection	A reflection creates a mirror image of a figure. It does not affect the shape or size of the figure.
Rotation	A rotation turns a figure around a fixed point. It does not affect the shape or size of the figure.

None of the three transformations affects the shape or size of the figure. Therefore, if we apply any sequence of translations, reflections, and rotations to a figure, the shape and size of the figure remains unchanged. This means that an image of a sequence of translations, reflections, and rotations is congruent to the preimage.

Exercise

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