Use the drop-down menus to complete the proof. by the unique line postulate, you can draw only one segment,

A reflection is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is known as the reflection's axis (in dimension 2) or plane (in dimension 3).
A figure's mirror image in the axis or plane of reflection is its image by reflection.

See the attached figure for a better explanation:

1. By the unique line postulate, you can draw only one line segment: BC

Since only one line can be drawn between two distinct points.

2. Using the definition of reflection, reflect BC over l.

To find the line segment which reflects BC over l, we will use the definition of reflection.

3. By the definition of reflection, C is the image of itself and A is the image of B.

Definition of reflection says the figure about a line is transformed to form the mirror image.
Now, the CD is the perpendicular bisector of AB so A and B are equidistant from D forming a mirror image of each other.

4. Since reflections preserve length, AC = BC

In Reflection the figure is transformed to form a mirror image.
Hence the length will be preserved in case of reflection.

Therefore, the reflection of BC over I is shown.

Know more about reflection here:

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The question you are looking for is here:

C is a point on the perpendicular bisector, l, of AB. Prove: AC = BC Use the drop-down menus to complete the proof. By the unique line postulate, you can draw only one segment, Using the definition of, reflect BC over l. By the definition of reflection, C is the image of itself and is the image of B. Since reflections preserve , AC = BC.