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E11 make generalizations about the rotational symmetry property of squares and rectangles and apply them.

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Title: E11 make generalizations about the rotational symmetry property of squares and rectangles and apply them.


1
E11 make generalizations about the rotational
symmetry property of squares and rectangles and
apply them.
2
Lets Review What are the properties of squares
that you already know?
  • A square is a quadrilateral.
  • A square has four congruent side lengths.
  • A square has four equal angles.
  • A square is a special type of rhombus.
  • A square is a parallelogram.
  • Each angle in a square measures 90 degrees.
  • The diagonals of a square are equal in length
    bisect each other intersect to form four right
    angles and combined with the previous properties
    this means they are perpendicular-bisectors of
    each other are bisectors of the vertex angles
    of the square, thus forming 45 degree angles and
    form four congruent isosceles right triangles

3
Now lets investigate another property of squares
  • Use a square from the pattern blocks, and mark
    one of its vertices with a chalk dot.
  • Next, carefully trace the block to make a square
    on a sheet of paper.
  • With the square block placed inside its picture,
    rotate it clockwise with the centre of rotation
    being the centre of the square (intersection
    point of its two diagonals) until it perfectly
    matches its picture again.
  • Notice that the marked vertex is at the next
    corner.
  • Repeat this rotation. How many times does the
    square appear in four identical positions during
    one complete 360-degree rotation?
  • The answer is 4, and the square is said to have
    rotational symmetry of order 4.

4
Rotational Symmetry of a Square
5
Lets Review What are the properties of
rectangles that you already know?
  • A rectangle is a quadrilateral.
  • A rectangle has four equal angles.
  • A rectangle is a special type of parallelogram
    with all 90- degree angles.
  • The diagonals of a rectangle are are equal in
    length bisect each other form two pairs of
    equal opposite angles at the point of
    intersection form two angles at each vertex of
    the rectangle that sum to 90 degrees and have the
    same measures as the two angles at the other
    vertices and
  • form two pairs of congruent isosceles triangles

6
Now lets investigate another property of
rectangles
  • Make a rectangle from hard paper, and mark one of
    its vertices with a chalk dot.
  • Next, carefully trace the rectangle to make a
    second rectangle on a sheet of paper.
  • With the rectangle block placed inside its
    picture, rotate it clockwise with the centre of
    rotation being the centre of the rectangle
    (intersection point of its two diagonals) until
    it perfectly matches its picture again.
  • Notice that the marked vertex is at the next
    corner.
  • Repeat this rotation. How many times does the
    rectangle appear in four identical positions
    during one complete 360-degree rotation?
  • The answer is 2, and the rectangle is said to
    have rotational symmetry of order 4.

7
Rotational Symmetry of a Rectangle
8
Meet Some of the Members of the Quadrilateral
Family
http//regentsprep.org/Regents/math/quad/LQuad.htm
9
Student Activities
  • E11.1 Investigate to find out if a square is the
    only quadrilateral with rotational symmetry of
    order 4.
  • E11.2 Investigate what other quadrilaterals
    besides rectangles have rotational symmetry of
    order 2.
  • Which ones also have two lines of reflective
    symmetry?
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