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Symmetry and Reflections

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Symmetry and Reflections Objectives Real-World Symmetry Connection Line symmetry can be found in works of art and in nature. Some figures, like this tree, Others ... – PowerPoint PPT presentation

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Title: Symmetry and Reflections


1
Symmetry and Reflections
2
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.

3
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.

8
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!
9
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)
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