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Definition of Reflection and Basic Properties




 

Videos and solutions to help Grade 8 students how to reflect a figure and learn the basic properties of reflection.

New York State Common Core Math Grade 8, Module 2, Lesson 4.

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Lesson Plans and Worksheets for Grade 8

Lesson Plans and Worksheets for all Grades

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Common Core For Grade 8

Student Outcomes

• 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'.


Lesson Summary

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'.


Concept Development

The following animation demonstrates reflection of a plane about a line.

Reflect a plane about a line

Exercises

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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