Reflectional symmetry can easily be seen by examing figures with a
Mira. The Mira is a device constructed of red plastic
with a beveled lower edge. The Mira is manufactured by the Mira
Math Company, located in Canada. When using the Mira, it
should be held steady by the left hand, with the designation
"Mira Math Company"facing the user and at the upper edge
of the Mira. The Mira can be used to bisect segments,
construct perpendiculars to segments, and bisect angles. It is
possible to perform many of the functions of a compass and
straightedge using the Mira. The Mira should always
have the beveled edge facing the user. The edge is beveled so that a
pencil can be drawn along the edge to create lines in the proper
position.Use the Mira to bisect the segment shown below by placing the Mira so that it is perpendicular to the segment and about in the middle. Look through the Mira and line up the reflection of the endpoint in front of the Mira with the endpoint behind the Mira. When it is properly lined up, use a pencil to draw a short line along the front edge of the Mira. Bisect the angle shown below by placing the Mira so that it is between the rays of the angle. Move the Mira until the reflection of the ray in front falls directly on the ray behind the Mira. Draw a line along the front edge of the Mira. This will be the angle bisector.
Use the Mira to draw in the three angle bisectors for the triangle shown below. The three angle bisectors should intersect at the same point.
Use the Mira to draw in the three perpendicular bisectors of the sides of the triangle shown below. The three perpendicular bisectors should intersect at the same point.
A figure has reflectional symmetry when there is a line of symmetry that separates the figure into two parts, one of which is a mirror image of the other part. The Mira can be used to find the line of reflectional symmetry of such a figure. Place the Mira on the shape and move it until one half of the shape matches the reflection of the other half. With the beveled edge of the Mira toward you, draw a line along the bottom of the Mira. Some figures have more than one line of reflectional symmetry.
Draw in all lines of reflectional symmetry for each of the figures given below.
Draw hexagons that have exactly 1, 2, and 3 lines of reflectional symmetry.
| 1 line | 2 lines | 3 lines |
A figure has rotational symmetry if there is a point called the center of rotation around which the figure can be rotated so that it aligns with itself in less than one complete rotation of 360°. The angle of rotational symmetry is the smallest angle through which the figure must be rotated so that it aligns with itself. The order of rotational symmetry is the number of small rotations that must be made to return to the original orientation. Rotational symmetry can be investigated by tracing the figure on paper, and rotating the tracing paper until the figures are aligned.
Use a small sheet of tracing paper to copy each figure in turn, place the tracing over the original figure, and rotate to determine the order and the angle of rotational symmetry.
Draw hexagons that have rotational symmetry of order 2 and 3.
| Order 2 | Order 3 |
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