Core Concept Clarification
When studying axis symmetry, it is essential to clearly distinguish between 'properties' and 'relationships':
- axi-symmetric figure: refers toa singlefigure. If a planar figure can be folded along a straight line such that parts on either side perfectly overlap, the figure is called an axi-symmetric figure, and this line is itsaxis of symmetry.
- two figures are symmetric about an axis: refers totwogeometric relationship between two figures. If one figure can be folded along a straight line to perfectly coincide with another figure, then the two figures are said to be symmetric about that line.
Core Elements of Symmetry
The points that coincide after folding arecorresponding points, known assymmetric points. The most important geometric property of axis symmetry is:the axis of symmetry is perpendicular and bisects the segment connecting corresponding points.
Observe the mask, bridge, butterfly, and road sign in Figure 13.1-1. The sense of balance they convey stems from equal distances of elements on both sides from the central axis.
In the geometric construction shown in Figure 13.1-4, triangle $ABC$ is reflected across line $MN$ to generate triangle $A'B'C'$. This is the foundation for all complex geometric transformations (translation, rotation, reflection).