What does symmetry (line symmetry) mean?

*Any figure is said to have a line of symmetry, if on folding the figure about this line, the two parts of the figure exactly coincide.*

If you can reflect (or flip) a figure over a line and the figure appears unchanged, then the figure has reflection symmetry or line symmetry. The line that you reflect over is called the line of symmetry. A line of symmetry divides a figure into two mirror-image halves. *Reference:* https://www.learner.org

Line of symmetry of a Triangle: The division of triangles into scalene, isosceles, and equilateral can be thought of in terms of lines of symmetry.

- A scalene triangle is a triangle with no lines of symmetry
- Isosceles triangle has at least one line of symmetry and an
- Equilateral triangle has three lines of symmetry.

*Reference:* https://www.illustrativemathematics.org

Line of symmetry of quadrilaterals:

- The square has four lines of symmetry.
- The rectangle has only two, as it can be folded in half horizontally or vertically.
- The trapezoid has only a vertical line of symmetry.
- The parallelogram has no line of symmetry.

*Reference:* https://www.illustrativemathematics.org

Line of symmetry of polygons:

- A Regular Pentagon (5 sides) has 5 Lines of Symmetry.
- A Regular Hexagon (6 sides) has 6 Lines of Symmetry.
- A Regular Heptagon (7 sides) has 7 Lines of symmetry.
- A Regular Octagon (8 sides) has 8 Lines of Symmetry.

*Reference:* http://www.mathsisfun.com/

You can see the logic…. a polygon with sides will have number of lines of symmetry.

Line of symmetry for other objects:

*Kite shaped quadrilateral*: This only have one line of symmetry.
*Isosceles Trapezium*: It has only one line of symmetry.
*A semi-circle*: It has only one line of symmetry.
*A circle*: It has infinite number of line of symmetry.
*A line segment*: It has two lines of symmetry. One is the perpendicular bisector and the other one is the line segment itself.
*An angle*: The angle has one line of symmetry. This is the angle bisector.
*Letter A*: It has one line of symmetry.
*Letter H*: It has two line of symmetry.

Properties of a line of symmetry:

- The figure on any side of the line of symmetry is a mirror image of the figure on the other side of it.
- A line of symmetry of a polygon is a perpendicular bisector of every line segment joining a pair of corresponding points of the polygon.
- In symmetric polygons, the corresponding sides and the corresponding angles are congruent.

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