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Here is some recommended reading before getting started with this lesson.
For some geometric figures, it is possible to find a transformation that maps the figures onto themselves. In such cases, the transformation is called a symmetry of the figure.
The line symmetries of a square confirm the claim made previously that squares belong to a particular class of parallelograms.
Polygon | Number of Line Symmetries | Line Symmetry |
---|---|---|
Rectangles | 2 | Along the lines connecting midpoints of opposite sides |
Rhombi | 2 | Along the lines containing the diagonals |
Squares | 4 | Two along the lines connecting midpoints of opposite sides and two along the lines containing the diagonals |
Notice that two symmetries of the square correspond to the rectangle's symmetries and the other two correspond to the rhombus symmetries. This suggests that squares are a particular case of rectangles and rhombi.