**diagonals are nor lines of symmetry**, but in a square they are.

Are Lingayats shudras?

**are lingayats brahmins**.

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**Rhombus**. A rhombus is a special kite with two axes of symmetry. The diagonals of a rhombus bisect each other at right angles. The diagonals of a rhombus bisect the corner angles.

Lines of symmetry can be **vertical**, horizontal or diagonal. The line of symmetry produces reflections that coincide.

It should be noted that for a rectangle, **the diagonals are not its lines of symmetry**. This is because, if a rectangle cut along its diagonals will not superimpose perfectly as the sides will be of different measurement.

Line symmetry in regular polygons The number of lines of symmetry in a regular polygon **is equal to the number of sides**.

Two shapes that have no lines of symmetry are the **scalene triangle** and an irregular quadrilateral.

When you reflect the regular pentagon below across line f, the pentagon will look exactly the same. Without labeled points, it will be impossible to tell the difference between the original pentagon and its image. This means that **the pentagon has reflection symmetry**.

**No**! Only regular polygons with an even number of vertices will . have point symmetry.

Parallelogram | Number of symmetry lines | Symmetry lines |
---|---|---|

Rhombus | 2 | Both its diagonals dividing it into two identical halves. |

In a rectangle, the opposite sides are equal and parallel to each other and the adjacent sides are at a right angle. Thus, it can be folded one along its length, and once along its breadth, giving us two lines of symmetry. … Thus the diagonals are **not lines of symmetry** for a rectangle.

Answer: (a) There are **4 lines** of symmetry for the given figure.

Lines of Symmetry in a Square In a square, there are four lines of symmetry, each of which divides it into two identical parts. The **symmetry lines of a square are both its diagonals** and the lines joining the midpoints of its opposite sides (bisectors).

An Equilateral Triangle (3 sides) has 3 Lines of Symmetry | |
---|---|

A Square (4 sides) has 4 Lines of Symmetry | |

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 |

Shape | # of Sides |
---|---|

Rectangle | 4 |

Quadrilateral | 4 |

Pentagon | 5 |

Hexagon | 6 |

The square has **four lines of symmetry**, indicated in gray in figure 1. There are the two axis and the two lines y = x and y = x. If we turn the square 180 about one of these lines, we get a symmetry.

Symmetries in regular polygons The order of rotational symmetry and the number of lines of symmetry of any regular polygon **is equal to the number of sides**.

There are **5 lines** of symmetry in a regular pentagon.

So, there are **8 lines** of symmetry of the regular octagon.

Irregular polygon: **Most irregular polygons do not have line symmetry**. However, some of them do. Look at the rectangle and the isosceles triangle. A rectangle has two lines of symmetry, and an isosceles triangle has one line of symmetry.

A shape can have more than one line of symmetry. Thus a **rectangle** has two lines of symmetry, an equilateral triangle has three lines of symmetry, and a square has four. A circle has an infinite number of lines of symmetry since it can be folded about any diameter.

**An isosceles triangle**: In the figure there is one line of symmetry.

A **rectangle** has two lines of symmetry.

An equilateral triangle has three lines of symmetry. It has rotational symmetry of order 3. It has three equal sides.

**Yes**, there is implication between lines of symmetry and point symmetry.

Therefore, all the diagonals of **a pentagon are equal**. = 108°. Therefore, each interior angle of a regular pentagon is three times of each exterior angle of a regular decagon.

Lesson Summary A pentagon is a **polygon** with five sides and five angles and can be either a regular or irregular polygon, depending on the measurements of its sides and angles.

A **polygon having equal sides and equal angles** is a regular polygon.

It has **4 lines** of symmetry – two diagonals and two lines running through the central points of opposite sides.

To recall, a rhombus is a 2-dimensional geometric figure whose all sides are equal. Unlike a square, the angles of a rhombus are not 90 degrees. So, the number of lines of symmetry are different for both **square** and rhombus. A rhombus has only two lines of symmetry, whereas a square has 4.

So **the square has four lines of symmetry**. The rectangle has only two, as it can be folded in half horizontally or vertically: students should be encouraged to try to fold the rectangle in half diagonally to see why this does not work.

Since there are **an infinite number of lines** through the center, the circle has an infinite number of lines of symmetry. When the circle is folded over a line of symmetry, the parts of the circle on each side of the line match up.

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** while an isosceles triangle has at least one line of symmetry and an equilateral triangle has three lines of symmetry.

There are **4 lines** of symmetry for the given figure.

A **scalene triangle**, parallelogram, and a trapezium are three examples of shapes with no line of symmetry.

Also, the upper half and the lower half can be divided into two equal halves by the line of symmetry. Therefore, we can see that in a double headed arrow there are **two lines of symmetry**.

The diagonals of a square bisect its angles. Opposite sides of a square are both parallel and equal in length. … All four sides of a square are equal. The diagonals of a square **are equal**.

A regular square has 4 sides and **4 lines** of symmetry. The number of lines of symmetry in a regular polygon is equal to the number of sides. There are 4 lines of symmetry in a regular square.

The diagonals of squares are equal to each other, they bisect each other, and they are **perpendicular** to each other.

A regular hexagon with six equal sides has **six lines** of symmetry. For all regular polygons, the number of lines of symmetry is equal to the number of sides. That is an equilateral triangle has 3 lines of symmetry, a square has 4 lines of symmetry, similarly a regular hexagon has 6 lines of symmetry.

A regular dodecagon is a figure with sides of the same length and internal angles of the same size. It has **twelve lines** of reflective symmetry and rotational symmetry of order 12.