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Identify lines of symmetry

A line of symmetry is a line that divides a plane figure into two congruent mirror-image halves: each point on one side corresponds to a point on the other at the same perpendicular distance from the line. Figures may have one, several, or no lines of symmetry, oriented vertically, horizontally, or diagonally; apparent visual balance alone does not establish symmetry.

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 check for a line of symmetry:

  1. Imagine folding the figure along the possible line.
  2. Check whether both halves match exactly.
  3. Make sure matching points are the same perpendicular distance from the line.

Example

A rectangle is 88 units wide and 44 units tall. How many lines of symmetry does it have?

  1. Draw a vertical line through the middle of the rectangle.
    This line divides the width into two equal parts of 44 units. Folding along it makes the left and right halves match.
    So, this is a line of symmetry.

  2. Draw a horizontal line through the middle of the rectangle.
    This line divides the height into two equal parts of 22 units. Folding along it makes the top and bottom halves match.
    So, this is also a line of symmetry.

  3. Check a diagonal line from one corner to the opposite corner.
    Folding along a diagonal would not make the two halves match because the rectangle is wider than it is tall.

Therefore, the rectangle has 22 lines of symmetry: one vertical line and one horizontal line.

Learn by doing: Identify lines of symmetry

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2D Shape (Picture) Line Symmetry - Is This a Line of Symmetry


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