Line Symmetry

Pre-Algebra · Axiom Academy

A figure has line symmetry when you can fold it along a line and the two halves land exactly on top of each other. A figure has line symmetry if you can fold it along a straight line so the two halves match exactly. That fold line is the line of symmetry , and one half is a perfect mirror image of the other. Watch the right half of this heart fold across the dashed line and land squarely on the left half. Not every fold line is a line of symmetry. A line only counts if the halves match when folded. Here the same rectangle is tested two ways: a vertical fold down the middle, and a fold along the diagonal. Watch which one lands cleanly and which one overshoots. Folding left onto right, the two halves cover each other exactly. The halves match, so this is a line of symmetry. Folding across the diagonal, the long side falls past the short side. The halves do not match, so a rectangle's diagonal is not a line of symmetry. To check any candidate fold line: imagine folding the figure along it. If the two halves land exactly on each other, it is a line of symmetry. If even one edge overshoots, it is not. 3. Counting the Lines of Symmetry Different figures pass the fold test along different numbers of lines — some many, some just one, some none at all. Watch each shape below reveal every fold line that makes its halves match, with a running count. 2 fold lines through opposite midpoints plus 2 along the diagonals. All four make the halves match.

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