Question

symmetry assignment

complete the following problem using complete sentences.

1. state the definition of reflection symmetry in your own words.
2. state the definition of rotational symmetry in your own words.
3. explain how point symmetry is an example of rotational symmetry.

for each part, draw a single image/shape that satisfies the following descriptions.

1. horizontal line symmetry, but not any other symmetry (meaning the image/shape has only horizontal symmetry and nothing else).
2. vertical line symmetry, but not any other symmetry.

Explanation:

Define reflection symmetry

Using the Reflection Symmetry knowledge point
Reflection symmetry occurs when a shape can be divided by a line (the line of symmetry) such that one half is a perfect mirror image of the other half.

Define rotational symmetry

Using the Rotational Symmetry knowledge point
Rotational symmetry exists when a shape can be rotated about a central point by an angle of less than \(360^\circ\) and still look exactly the same as its original position.

Relate point symmetry to rotational symmetry

Using the Point Symmetry and Rotational Symmetry knowledge points
Point symmetry is a specific type of rotational symmetry where a shape looks exactly the same when rotated \(180^\circ\) (half a turn) around its central point.

Design a shape with only horizontal line symmetry

To have only horizontal line symmetry, a shape must be symmetric across a horizontal axis but asymmetric vertically and have no rotational symmetry. An isosceles trapezoid oriented sideways (pointing left or right) satisfies this condition.

Design a shape with only vertical line symmetry

To have only vertical line symmetry, a shape must be symmetric across a vertical axis but asymmetric horizontally and have no rotational symmetry. A standard upright isosceles triangle satisfies this condition.

Answer:

Question 1

Reflection symmetry is a characteristic of a shape where it can be split by a line into two halves that are mirror images of each other.

Question 2

Rotational symmetry is a characteristic of a shape where it can be rotated around a central point by some angle less than \(360^\circ\) and appear completely unchanged.

Question 3

Point symmetry is a special case of rotational symmetry because it occurs when a shape matches itself exactly after a rotation of precisely \(180^\circ\) about its center.

Question 4

An example of a shape with only horizontal line symmetry is a sideways isosceles trapezoid:

      +------+
     /        \
    +----------+

Question 5

An example of a shape with only vertical line symmetry is an upright isosceles triangle:

        /\
       /  \
      /    \
     +------+