Let's evaluate each statement related to reflections:
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An image created by a reflection will always be congruent to its pre-image.
- True: Reflections preserve distances and angles, which means the image will be congruent to the pre-image.
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An image and its pre-image are always the same distance from the line of reflection.
- True: By definition, the image point is located directly opposite the pre-image point at the same distance from the line of reflection.
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If a point on the pre-image lies on the line of reflection, the image of that point is the same as the pre-image.
- True: If a point is on the line of reflection, it remains unchanged in the reflection.
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The line of reflection is perpendicular to the line segments connecting corresponding vertices.
- True: The line of reflection is always perpendicular to the line segments that connect corresponding points (or vertices) in the pre-image and image.
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The line segments connecting corresponding vertices are all congruent to each other.
- True: Since reflections preserve distances, the segments connecting corresponding points (matching pre-image and image points) will be the same length.
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The line segments connecting corresponding vertices are all parallel to each other.
- False: The line segments connecting corresponding vertices are not necessarily parallel; they can converge towards or diverge from the line of reflection depending on the orientation of the pre-image.
So, the true statements are: 1, 2, 3, 4, and 5.
1 answer