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Identify lines of symmetry

A line of symmetry is a line in the plane that divides a two-dimensional figure into mirror-image halves: reflection across the line maps every point of the figure to a point of the same figure, with corresponding points the same distance from the line. This understanding supports identifying and counting lines of symmetry in familiar polygons and composite figures, while excluding rotational symmetry and more advanced algebraic or higher-dimensional generalizations.

Detailed Explanation: Identify lines of symmetry

A line of symmetry divides a figure into two halves that are exact mirror images. If you folded the figure along the line, the two halves would match perfectly.

To test a possible line:

  1. Draw or imagine the line through the figure.
  2. Check whether the two sides have the same shape and size.
  3. Make sure matching points are the same distance from the line.
  4. If the halves do not match, the line is not a line of symmetry.

Example: How many lines of symmetry does a rectangle that is not a square have?

Imagine a rectangle that is longer than it is tall.

  • A vertical line through the center divides the rectangle into two matching halves. The left and right sides mirror each other, so this is a line of symmetry.
  • A horizontal line through the center also divides the rectangle into two matching halves. The top and bottom sides mirror each other, so this is another line of symmetry.
  • A diagonal line does not work. Folding along a diagonal would not make the two halves match because the rectangle is longer in one direction than the other.

Therefore, the rectangle has

2\boxed{2}

lines of symmetry: one vertical line and one horizontal line through its center.

Learn by doing: Identify lines of symmetry

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    2D Shape Symmetry - Where Is Line of Symmetry

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