# Class 5 symmetry worksheet with answers

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﻿symmetry and patterns worksheet class 5 with answers. Download maths patterns for class 5 worksheet including questions on rotational symmetry, mirror symmetry, questions patterns and more.

What is line of symmetry?

When the image formed is of the same shape and size and is at the same distance from the mirror line as the object. The line is called a mirror line or line of symmetry or line of reflection.

FAQ's

What is rotational symmetry or Who discovered symmetry?

Rotational means turning, In geometry rotational is turning any figure around a point, which is called the point of symmetry. A figure which looks the same after rotating it half or quarter etc is called rotational symmetry.

Difference between pattern and symmetry

A pattern can be symmetrical or asymmetric in nature, symmetry means an object is symmetry in terms of mirror reflection or maybe rotational symmetric in nature

who invented symmetry

Symmetry and pattern are related concepts in mathematics, art, and design.

Symmetry refers to the property of an object or image that remains unchanged when it is reflected, rotated, or translated. Objects that have symmetry are said to be symmetric. There are several types of symmetry, including reflectional symmetry, rotational symmetry, and translational symmetry.

Patterns are a type of visual design that involves the repetition of elements or motifs. Patterns can be found in nature, architecture, textiles, and other forms of art and design. They can be used to create a sense of movement, rhythm, and harmony in a composition.

Both symmetry and pattern are important concepts in mathematics, with applications in fields such as physics, engineering, and computer science. They are also used extensively in art and design as a means of creating visually pleasing and interesting compositions.

who discovered symmetry

Symmetry has been studied and observed by humans for thousands of years, so it is difficult to say who "discovered" it. Many ancient cultures, such as the Egyptians and Greeks, were known to have used symmetry in their art and architecture. The concept of symmetry was also studied by mathematicians and scientists in various cultures throughout history.

In the field of mathematics, the first known systematic study of symmetry was conducted by Euclid, a Greek mathematician who lived around 300 BCE. Euclid wrote a treatise called "The Elements," in which he discussed symmetry in the context of geometric figures.

In the 19th century, the study of symmetry was formalized and expanded upon by mathematicians such as Augustin-Louis Cauchy, Evariste Galois, and Niels Henrik Abel, who developed the theory of group and the concept of group action.

In the 20th century, the study of symmetry was further developed and expanded upon by scientists and mathematicians such as Hermann Weyl, Emmy Noether and many others, who introduced the concept of symmetry in physics, chemistry, engineering and other fields.

So, it could be said that symmetry has been discovered and studied by many cultures, mathematicians and scientists throughout history.

why 5 fold symmetry does not exist

In nature, five-fold symmetry is rare because it is not as energetically favorable as other types of symmetry. This is because most natural systems tend to minimize their energy, and five-fold symmetry requires more energy to maintain than other types of symmetry.

In mathematics and physics, it is also argued that five-fold symmetry is not possible due to the mathematical properties of space. The five-fold symmetry does not exist in the three-dimensional Euclidean space, because it's not possible to divide a sphere into five equal parts with identical angles. In crystallography, five-fold symmetry is also not observed in crystals. The most symmetric crystal structures are those that have rotational symmetry of two, three, four, and six, which are known as the Platonic solids. While the five-fold symmetry is not possible in crystals, quasicrystals, which are not periodic but have long-range order, have been found to have five-fold symmetry. In conclusion, while five-fold symmetry is not commonly observed in nature, it is not impossible, but it is less favourable in terms of energy requirements and mathematical properties of space and is not observed in crystals.

how much symmetry does a circle have? A circle has infinite rotational symmetry. This means that if you rotate a circle by any angle, it will always look the same. The rotational symmetry of a circle is defined as an infinite number of identical rotations around its centre. A circle doesn't have any reflectional symmetry or translational symmetry. A reflectional symmetry is a symmetry with respect to a mirror plane and a translational symmetry is a symmetry with respect to a translation.It is also worth noting that a circle is also invariant under transformations such as scaling, dilation and rotation. This means that a circle will look the same after being scaled, dilated or rotated.

In summary, a circle has infinite rotational symmetry, but it has no reflectional symmetry or translational symmetry.

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