To determine the single transformation that proves congruence between two figures, we need more information about the specific figures in question. However, if you are looking for a general answer:
- Translation (1): Moves a figure without changing its size, shape, or orientation.
- Reflection (2): Flips a figure over a line, creating a mirror image.
- Rotation (3): Turns a figure around a fixed point, maintaining size and shape.
- Dilation (4): Changes the size of a figure but maintains its shape; this does not prove congruence.
Congruent figures can be obtained through translation, reflection, or rotation. Dilation does not preserve the size, so it doesn't prove congruence.
If only one transformation is needed to show congruence, it would be either 1, 2, or 3. You would need to analyze the figures to determine which transformation applies.
If you can provide specific details about the figures' positions and orientations, I can help you identify the correct transformation.