Reflections and rotations of shapes

Reflections and rotations of shapes

Lessons

In this lesson, we will learn:

  • How to draw reflections on a grid with vertical, horizontal, or diagonal mirror lines
  • How to find order of rotational symmetry for shapes with multiple symmetry lines
  • How to rotate shapes around a point 90°, 180°, 270°, and 360° clockwise or counter-clockwise

Notes:

  • For line symmetry, a mirror test check if reflected halves match
Reflections and Rotations of Shapes
  • When drawing reflections of shapes, a grid and a line of symmetry are used
    • For reflections, the line of symmetry will be called the “mirror line” instead
    • There can be vertical, horizontal, and diagonal mirror lines
Reflections and Rotations of Shapes
    • Choose some exact points of the original shape on the grid
    • To draw the reflection of these points, they must be the same distance away from the mirror line as the original points (perpendicularly)
Reflections and Rotations of Shapes

  • Another type of symmetry is called rotational symmetry
    • If a shape has multiple lines of symmetry: when you spin it around in a full circle (360°), it will look exactly the same more than once

Ex. a triangle has 3 lines of symmetry; rotating a full circle, it matches the original 3 times
Reflections and Rotations of Shapes
    • Therefore, the order of rotational symmetry for this regular triangle is = 3

  • When rotating shapes, the shape will be spun around a point (usually the middle):
    • either clockwise or counter-clockwise
    • To one of 4 main rotation angles: 90°, 180°, 270°, and 360°

Ex. Rotate the shape of the letter “P” clockwise 90°, 180°, and 270° around the point
Reflections and Rotations of Shapes
  • Introduction
    Introduction to Reflections and Rotations of Shapes:
    a)
    Drawing reflections (mirror images) on a grid

    b)
    What is rotational symmetry?

    c)
    Rotating shapes around a point (four main rotational angles)

    d)
    Special example of reflecting and rotating a shape


  • 1.
    Drawing reflections on a grid - 1
    Draw the mirror image after the shape is reflected across the mirror line (dotted line).
    a)
    Reflections and Rotations of Shapes

    b)
    Reflections and Rotations of Shapes

    c)
    Reflections and Rotations of Shapes


  • 2.
    Drawing reflections on a grid - 2
    Draw the reflections of both the lines and the points across the mirror line (dotted line).
    a)
    Reflections and Rotations of Shapes

    b)
    Reflections and Rotations of Shapes

    c)
    Reflections and Rotations of Shapes


  • 3.
    Rotational symmetry
    Does the picture have rotational symmetry? Yes or No.
    a)
    Reflections and Rotations of Shapes

    b)
    Reflections and Rotations of Shapes

    c)
    Reflections and Rotations of Shapes

    d)
    Reflections and Rotations of Shapes


  • 4.
    Order of rotational symmetry
    What is the order of rotational symmetry?
    • How many times does the shape look the same in one rotation?
    a)
    Reflections and Rotations of Shapes

    b)
    Reflections and Rotations of Shapes

    c)
    Reflections and Rotations of Shapes


  • 5.
    Rotating shapes 90°, 180°, 270° or 360°
    Draw what it will look like if you rotate the shape:
    a)
    Reflections and Rotations of Shapes
    1. 90° CW
    2. 90° CCW
    3. 180° CW

    b)
    Reflections and Rotations of Shapes
    1. 270° CW
    2. 180° CCW
    3. 360° CW


  • 6.
    Recognizing reflections and rotations of shapes
    Circle the pairs that are correct.
    a)
    Which pairs are possible rotations of each other? Reflections and Rotations of Shapes

    b)
    Which pairs are possible reflections of each other? Reflections and Rotations of Shapes

    c)
    Which pairs have the line of reflection drawn properly? Reflections and Rotations of Shapes