To determine the single rigid transformation that maps triangle \( \triangle ABC \) onto triangle \( \triangle EDC \), we need to analyze how the geometric properties relate between the two triangles, based on their positions and orientations.
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Dilation: This is a transformation that changes the size of the triangle but keeps the shape the same. A dilation does not maintain the exact orientation unless the scale factor is equal to \( 1 \). Since the question implies an exact mapping, this is typically not the case.
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Rotation: This involves turning the shape around a specific point. If the triangles are oriented in different directions, a rotation may align them correctly.
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Translation: This is a sliding movement in any direction. If the triangles are the same size and shape but located in different positions, a translation could map one triangle to the other.
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Reflection: This involves flipping the triangle over a line. If one triangle is a mirror image of the other, this transformation would map them.
Without the visual reference of the triangles, I can't definitively tell which transformation applies. However, you can apply these rules:
- If the triangles are the same size and shape, but one has been moved to a different location without changing its orientation, the transformation is a translation.
- If they are the same size and shape but oriented differently, the transformation could be a rotation or possibly a reflection if one is a mirror image of the other.
Based on standard configurations, if triangle \( \triangle ABC \) and triangle \( \triangle EDC \) have the same dimensions and orientation, and aligned properly, it will usually be rotation or reflection.
If you can provide the arrangement or more characteristics of the triangles (like their vertices' coordinates or other specific details), I can give a more precise answer. For your current question, evaluate if the triangles are simply translated or if they've been flipped or rotated.
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