2 lines of symmetry Lines of Symmetry in a Rectangle. A rectangle has 2 lines of symmetry which divides it into two identical parts.

Contents

- 1 Why does a rectangle only have 4 lines of symmetry?
- 2 How many shapes have infinite lines of symmetry?
- 3 Why is a rectangle not the only shape with two lines of symmetry?
- 4 Which shape has 6 lines of symmetry?
- 5 What 4 sided shapes have 2 lines of symmetry?
- 6 Which shape has more than 4 lines of symmetry?

### Does a rectangle have 2 or 4 lines of symmetry?

What Are Lines of Symmetry in a Rectangle? – A rectangle has two lines of symmetry, one horizontal and one vertical. Each of these lines divide the rectangle into two identical parts. In simple words, you can fold a rectangle into half either horizontally or vertically.

- In geometry, a symmetrical figure is a figure that can be folded along a line such that the two parts are identical.
- The line through which we fold is known as the line of symmetry.
- A line of symmetry always cuts the shape into two mirror images.
- A rectangle is a quadrilateral in which opposite sides are parallel and equal.

It has 4 right angles $(90^\circ)$. Since a rectangle is a 2-D shape, it is characterized by two dimensions, length, and width. Length is the longer side of the rectangle and width is the shorter side.

## Why does a rectangle only have 4 lines of symmetry?

Conclusion – We learned in this article. A rectangle’s lines of symmetry are the lines that divide the rectangle into two identical halves. A rectangle has 2 symmetry lines. The first is drawn horizontally, while the second is drawn vertically. It should be noted that a rectangle’s diagonals are not considered lines of symmetry because they do not divide the rectangle into equal and identical halves.

#### How many lines of symmetry does a regular rectangle have?

Rectangle –

- A rectangle has two lines of symmetry.
- It has rotational symmetry of order two.

### Can a rectangle have more than 2 lines of symmetry?

Solution – The lines of symmetry for each of the four quadrilaterals are shown below: When a geometric figure is folded about a line of symmetry, the two halves match up so if the students have copies of the quadrilaterals they can test lines of symmetry by folding. For the square, it can be folded in half over either diagonal, the horizontal segment which cuts the square in half, or the vertical segment which cuts the square in half.

- 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.
- The trapezoid has only a vertical line of symmetry.
- The parallelogram has no lines of symmetry and, as with the rectangle, students should experiment with folding a copy to see what happens with the lines through the diagonals as well as horizontal and vertical lines.

The lines of symmetry indicated are the only ones for the figures. One way to show this is to note that for a quadrilateral, a line of symmetry must either match two vertices on one side of the line with two vertices on the other or it must pass through two of the vertices and then the other two vertices pair up when folded over the line.

### Does a rectangle have 4 symmetry?

Video Lesson on Properties of rectangles – A rectangle is a 4 sided polygon whose two opposite sides are equal and parallel. The angles of a rectangle are always 90 degrees and its diagonals are always equal. A rectangle has 2 lines of symmetry. The lines of symmetry in a rectangle cut its opposite sides into equal parts. Yes, a rectangle has rotational symmetry. A rectangle has rotational symmetry of 180° (Order 2). Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin! Select the correct answer and click on the “Finish” buttonCheck your score and answers at the end of the quiz Visit BYJU’S for all Maths related queries and study materials

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View Quiz Answers and Analysis : Lines of Symmetry in Rectangle (Definition and Order)

### Which shape has more than 4 lines of symmetry?

Shape | Number of lines of symmetry |
---|---|

(1) Isosceles triangle | (a) 6 |

(2) Square | (b) 5 |

(3) Kite | (c) 4 |

(4) Equilateral triangle | (d) 3 |

#### What has only 2 lines of symmetry?

Look at the shapes below. The symmetry of the shape on the left and its relationship to the shape on the right can be thought of in two ways:

Fold the left-hand shape along the central line. Then one side lies exactly on top of the other, and gives the shape on the right. Imagine a mirror placed along the central dotted line. The reflection in the mirror gives the other half of the shape.

This type of symmetry is called line symmetry, Any isosceles triangle has line symmetry. The dashed lines represent lines of symmetry, and each shape is said to be symmetrical about this line. The following all have line 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. Only eight of the possible lines of symmetry are indicated below. Some shapes, such as a scalene triangle, have no lines of symmetry – it is not possible to fold the shape about a line so that the two halves fit exactly on top of one another.

#### Can a triangle have 4 lines of symmetry?

IM Commentary – 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.

- This activity provides students an opportunity to recognize these distinguishing features of the different types of triangles before the technical language has been introduced.
- For finding the lines of symmetry, cut-out models of the four triangles would be helpful so that the students can fold them to find the lines.

This task is intended for instruction, providing the students with a chance to experiment with physical models of triangles, gaining spatial intuition by executing reflections. A word has been added at the end of the solution about why there are not other lines of symmetries for these triangles: this has been inserted in case this topic comes up in a class discussion but the focus should be on identifying the proper lines of symmetry.

#### What shape has no line of symmetry?

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

## How many shapes have infinite lines of symmetry?

IM Commentary – A circle has an infinite number of symmetries. This contrasts with polygons such as the triangles and quadrilaterals considered in 4.G Lines of symmetry for triangles and 4.G Lines of symmetry for quadrilaterals, The circle is, in some sense, the most symmetric two dimensional figure and it is partly for this reason that it is so familiar.

- Coins, clock faces, wheels, the image of the full moon in the sky: these are all examples of circles which we encounter on a regular basis.
- This is an instructional task that gives students a chance to reason about lines of symmetry and discover that a circle has an an infinite number of lines of symmetry.

Even though the concept of an infinite number of lines is fairly abstract, fourth graders can understand infinity in an informal way. Just as there is always a fraction between any two fractions on the number line, there is always another line through the center of the circle “between” any two lines through the center of the circle.

- The algebraic perspective, using the equation that defines a circle, and
- The geometric perspective, using the definition of reflections in terms of perpendicular lines.

This task includes an experimental GeoGebra worksheet, with the intent that instructors might use it to more interactively demonstrate the relevant content material. The file should be considered a draft version, and feedback on it in the comment section is highly encouraged, both in terms of suggestions for improvement and for ideas on using it effectively.

## Why is a rectangle not the only shape with two lines of symmetry?

Answer: Dave is not correct in statement that rectangle is only quadilateral having 2 lines of symmetry. Step-by-step explanation:

When an imaginary line divides the object in 2 equal haves, the object is called in symmetry,The rectangle is not the only figure having 2 lines of symmetr y as the square,rombus are also shapes having 2 lines of the symmetry. Thus dave is wrong in his statement.

## Which shape has 6 lines of symmetry?

A regular hexagon has 6 lines of symmetry. In a regular polygon the lines of symmetry are equal to the number of sides.

#### Which shapes has 4 equal sides and 2 lines of symmetry?

Rotational Symmetry of a Rhombus – A rhombus has four equal sides but of varying angles. A rhombus has two lines of symmetry (vertical and horizontal), an order of two, and the angle of rotation of 180 degrees.

## What 4 sided shapes have 2 lines of symmetry?

Rhombus –

- A rhombus has two lines of symmetry.
- It has rotational symmetry of order two.

- It has four equal sides.
- The opposite angles are equal.
- The opposite sides are parallel.
- The diagonals bisect each other at right angles.

## Which shape has more than 4 lines of symmetry?

Shape | Number of lines of symmetry |
---|---|

(1) Isosceles triangle | (a) 6 |

(2) Square | (b) 5 |

(3) Kite | (c) 4 |

(4) Equilateral triangle | (d) 3 |