The Reflection Postulate

Almost a week ago, we have discussed about some properties of reflection. We have learned that the pre-image of a figure is congruent to its image. We have also observed that the pre-image and image mirror each other. We also say that the preimage and image are symmetric.

In this post, we learn formally the Reflection Postulate. There are five properties of reflection. They are the following.

Under reflection

  1. There is a 1-1 correspondence between points and their images. This means that each pre-image has exactly one image and each image comes from exactly one pre-image.
  2. If three points are collinear, then their images are collinear. Reflections preserve collinearity. The image of a line is a line.
  3. If B is between A and C, then the image of B is between the images of A and C. Reflections preserve betweenness. The image of a line segment is a line segment.
  4. The distance between two pre-images equals the distance between their images. Reflections preserve distance.
  5. The image of an angle is an angle of the same measure. Reflections preserve angle measure.

To summarize the list above, we can say that reflections preserve angle measure, betweenness, collinearity and distance.

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