SLT 19 Construct a square and
describe its rotational and
reflectional symmetry.
MCPS
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Printed: May 20, 2014
AUTHOR
MCPS
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C HAPTER
Chapter 1. SLT 19 Construct a square and describe its rotational and reflectional symmetry.
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SLT 19 Construct a square
and describe its rotational and
reflectional symmetry.
Guidance
A square is a quadrilateral with four right angles and four congruent sides. All squares are rectangles and rhombuses.
Watch This
http://www.mathopenref.com/constsquare.html Constructing a square
How to Construct a Square
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Rotational symmetry is present when a figure can be rotated (less than 360◦ ) such that it looks like it did before the
rotation. The center of rotation is the point a figure is rotated around such that the rotational symmetry holds.
Example A
Does a square have rotation symmetry?
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Chapter 1. SLT 19 Construct a square and describe its rotational and reflectional symmetry.
Solution: Yes, a square can be rotated 90◦ counterclockwise (or clockwise) about its center and the image will be
indistinguishable from the original square.
Example B
How many angles of rotation cause a square to be carried onto itself?
Solution: Rotations of 90◦ , 180◦ and 270◦ counterclockwise will all cause the square to be carried onto itself.
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The square can be rotated 4 times and still look the same.
Reflectional Symmetry is present when a figure has one or more lines of symmetry. A square has four lines of
symmetry.
Example C
Does a square have reflection symmetry?
Solution: Yes, because there exists at least one line of reflection that carries the square onto itself. Like a rectangle,
a line through the midpoints of opposite sides will be a line of symmetry.
Example D
How many lines of symmetry does a square have?
Solution: A square has 4 lines of symmetry. Lines through the midpoints of opposites sides and lines through
opposite vertices are all lines of symmetry.
Guided Practice
Draw a square. Draw in the diagonals of the square. Make at least one conjecture about the diagonals of the square.
Answer:
To make a conjecture means to make an educated guess. There are a few conjectures you might make about the
diagonals of a square. These conjectures will be proved in a later concept. Here are some possible conjectures:
•
•
•
•
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diagonals of a square are congruent
diagonals of a square are perpendicular
diagonals of a square bisect each other (cut each other in half)
diagonals of a square bisect the angles (cut the 90◦ angles in half)
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Chapter 1. SLT 19 Construct a square and describe its rotational and reflectional symmetry.
Practice
Use the markings on the shape below to identify the shape. Then, solve for x. Note: pictures are not drawn to scale.
References
1. . . CC BY-NC-SA
2. . . CC BY-NC-SA
3. . . CC BY-NC-SA
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