iven: 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.
2 answers:
Answer:
For a clearer understanding, refer to the attached figure:
Step-by-step breakdown:
1. According to the unique line postulate, only one line segment can be created: BC
This is because a single line can only connect two distinct points.
2. Utilizing the definition of reflection, reflect BC across l.
To identify the line segment reflected over l, we will apply the reflection definition.
3. Based on the reflection definition, C remains as its own image and A represents the image of B.
The reflection definition states that a figure is transformed into a mirror image around a line. Thus, CD serves as the perpendicular bisector of AB, which makes A and B equidistant from D, producing their mirror images.
4. Because reflections maintain length, we find that AC = BC
In a reflection, the figure transforms to create a mirror image, ensuring the lengths remain unchanged.
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