Symmetry and Reflections

1
Symmetry and Reflections
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Objectives

• Describe and identify lines of symmetry.
• Create reflections on a coordinate plane.

Vocabulary

• If a line can be drawn through a figure so that
  the two halves match like a mirror image the
  figure has line symmetry.
• A reflection is a movement that flips an entire
  figure over a line called a line of reflection.

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Real-World Symmetry Connection

• Line symmetry can be found in works of art and in
  nature.
• Some figures, like this tree, Others, like
  this snowflake,
• have only one line of symmetry. have multiple
  lines of symmetry.

Vertical, horizontal, diagonal symmetry
Vertical symmetry
4
Paper Practice

• Using your ruler, draw all lines of symmetry for
  each figure.
• When you finish, check your results with your
  partner.
• Expand your mind how many lines of symmetry does
  a circle have?

5
Reflections

• Look at yourself in a mirror!
• How does your reflection respond as you step
  toward the mirror? away from the mirror?
• When a figure is reflected, the image is
  congruent to the original.
• The actual figure and its image appear the same
  distance from the line of reflection, here the
  mirror.

6
Discovery Learning

• Use GeoGebra to explore how a point is reflected
  over the y-axis on the coordinate plane.
• Try moving point A on both sides of the y-axis.
• In your notebook, list 3 positions of A and its
  corresponding reflection at A.
• Summarize your findings.
• When finished, discuss with your neighbor.
• Follow the above steps to reflect a point over
  the x-axis.
• What is similar/different about your findings?

7
Reflecting a Point

• We learned how to graph a point as an ordered
  pair on the coordinate plane.
• The point A(1, -2) is in quadrant IV.

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To graph the reflection of point A(1,-2) over the
y-axis
1.Identify the y-axis as the line of symmetry
(the mirror). 2. Point A is 1 unit to the right
of the y-axis, so its reflection A is 1 unit to
the left of the y-axis. We discovered an
interesting phenomenon simply change the sign of
the x-coordinate to reflect a point over the
y-axis!
Similarly, to graph the reflection of a point
over the x-axis, simply change the sign of the
y-coordinate!
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Reflecting a Figure

• Use these same steps to reflect an entire figure
  on the coordinate plane
• Identify which axis is the line of symmetry (the
  mirror).
• Individually reflect each endpoint of the figure.
• Connect the reflected points.
• Lets try on paper! (Practice 10-7)