• Students know the definition of reflection and perform reflections across a line using a transparency.
• Students show that reflections share some of the same fundamental properties with translations (e.g., lines map to lines, angle and distance preserving motion, etc.).
• Students know that reflections map parallel lines to parallel lines.
• Students know that for the reflection across a line L, then every point P, not on L, L is the bisector of the segment joining P to its reflected image P'.
A reflection is another type of basic rigid motion.
Reflections occur across lines. The line that you reflect across is called the line of reflection.
When a point, P, is joined to its reflection, P', the line of reflection bisects the segment, PP'.
The following animation demonstrates reflection of a plane about a line.
Reflect a plane about a line
1. Refect triangle ABC and Figure D across line L. Label the reflected images.
2. Which figure(s) were not moved to a new location on the plane under this transformation?
3. Reflect the images across line L. Label the reflected images.
4. Answer the questions about the previous image.
a. Use a protractor to measure the reflected ∠ ABC
b. Use a ruler to measure the length of image of IJ after the reflection.
5. Reflect Figure R and triangle EFG across line L. Label the reflected images.
Basic Properties of Reflections:
(Reflection 1) A reflection maps a line to a line, a ray to a ray, a segment to a segment, and an angle to an angle.
(Reflection2) A reflection preserves lengths of segments.
(Reflection 3) A reflection preserves degrees of angles.
If the reflection is across a line L and P is a point not on L, then L bisects the segment PP’, joining P to its reflected image P’. That is, the lengths of OP and OP’ are equal.
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