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The construction of the symmetrical of a point of a line, of a figure with respect to an axis.
I. Symmetrical figures
Two figures are symmetrical about a line if they overlap by folding along that line.
This line is called theaxis of symmetry.
II. Symmetric of a point.
1. definition of the symmetric.
The symmetric of a point A with respect to a line (d) is the point A’, such that the line (d) is the perpendicular bisector of the segment [AA’] (i.e. such that (d) is the perpendicular to the segment [AA’] in its middle).
2. Construction of the symmetric with the square and the graduated rule.
3. Construction of the symmetric with the compass.
III. Properties of axial symmetry
The symmetric of a line about an axis is a line.
Axial symmetry preserves the alignment.
The symmetric of the middle of a segment is the middle of the symmetric segment.
The symmetry of a circle about an axis is a circle of the same radius. The centers of the circles are symmetrical about this axis.
To construct the symmetric of a complex figure, we break it down into usual figures and construct the symmetric of each of them.
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