Which statements are true about reflections? Check all that apply.An image created by a reflection will always be congruent to its pre-image.An image and its pre-image are always the same distance from the line of reflection.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.The line of reflection is perpendicular to the line segments connecting corresponding vertices.The line segments connecting corresponding vertices are all congruent to each other.The line segments connecting corresponding vertices are all parallel to each other.
Answer
A
An image created by a reflection will always be congruent to its pre-image.
B
An image and its pre-image are always the same distance from the line of reflection.
C
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.
D
The line of reflection is perpendicular to the line segments connecting corresponding vertices.
E
The line segments connecting corresponding vertices are all congruent to each other.
F
The line segments connecting corresponding vertices are all parallel to each other.
Explanation
A reflection preserves lengths, so the image is congruent to its pre-image. Each point and its reflected image lie the same distance from the line of reflection, and a point on that line stays fixed. The line of reflection is the perpendicular bisector of the segments joining corresponding points, so those segments are perpendicular to it and therefore parallel to one another. Their lengths can differ because they depend on how far each point is from the line, so statement E is not always true.
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