Question

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.

Explanation:

• Congruence: A reflection is a rigid transformation. Rigid transformations preserve the shape and size of a figure. So, an image created by a reflection will always be congruent to its pre - image.
• Distance from the line of reflection: By the definition of a reflection, for every point in the pre - image and its corresponding point in the image, the line of reflection is the perpendicular bisector of the segment joining the pre - image point and the image point. So, an image and its pre - image are always the same distance from the line of reflection.
• Point on the line of reflection: If a point lies on the line of reflection, then its reflection over that line is itself.
• Line of reflection and connecting segments: The line of reflection is perpendicular to the line segments connecting corresponding vertices. This is a property of reflections.

• Congruence of connecting segments: The line segments connecting corresponding vertices are not necessarily congruent to each other. For example, if you reflect a non - regular polygon, the lengths of these connecting segments can vary.
• Parallelism of connecting segments: The line segments connecting corresponding vertices are not necessarily parallel to each other. Consider a reflection of a non - symmetric figure across a non - special line.

Answer:

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.