To determine the single rigid transformation that maps triangle \( \triangle ABC \) to triangle \( \triangle EDC \), we need to analyze the position and orientation of both triangles.
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Reflection: This transformation flips the triangle over a line (axis of reflection). If the triangles are mirror images across a line, reflection is the transformation.
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Translation: This transformation slides the triangle without changing its shape or orientation. If \( \triangle ABC \) can be moved to overlay \( \triangle EDC \) by sliding, translation is the transformation.
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Rotation: This transformation turns the triangle around a point (center of rotation). If \( \triangle ABC \) has been turned to align with \( \triangle EDC \), rotation is the correct answer.
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Dilation: This transformation changes the size of the triangle but maintains the shape. If \( \triangle ABC \) simply looks larger or smaller when comparing to \( \triangle EDC \), dilation is the transformation, but this does not maintain congruence.
Since the question is concerned with congruence, we should rule out dilation and focus on rigid transformations like reflection, translation, and rotation.
To accurately choose the transformation, we typically would analyze the images of the triangles. If you can visually confirm that triangle \( \triangle EDC \) is merely a flipped version of triangle \( \triangle ABC \), reflection would be the answer. However, if \( \triangle EDC \) can be reached by merely sliding \( \triangle ABC \) without flipping or rotating, then translation would be the appropriate choice. Rotation is required if the triangles are positioned differently in orientation but remain congruent.
In the absence of visuals, the answer would be determined by these relationships. Please provide more details or indicate the specific nature of how \( \triangle ABC \) and \( \triangle EDC \) are configured relative to each other for a definitive response.