The ideas of symmetry are covered in Chapter 14 of the NCERT syllabus for Class 7 Maths. You’ll learn how to memorize reflection symmetry, rotational symmetry, and rotational symmetry observations in 2-D objects. The concept of symmetry will be useful in all of our daily actions.
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NCERT Solutions for Class 7 Maths Chapter 14
What is the definition of symmetry?
In mathematics, symmetry is a crucial geometrical concept. The concept of symmetry is applied in practically every aspect of our daily lives. Any object that is divided into two identical halves becomes a mirror copy of itself. The two halves are said to be symmetrical to each other.
Facts:
- Regular polygons have the same number of sides as they do angles. They feature numerous symmetry lines or more than one.
- A square has four symmetry lines.
- A regular pentagon has five symmetry lines.
- A regular hexagon has six symmetry lines.
- An object rotates around a fixed point known as the center of rotation.
- The angle of rotation is the angle at which an object rotates.
- A half-turn is equal to [Equation]rotations.
- If an object looks exactly the same after being rotated, it is said to have rotational symmetry.
Line of Symmetry:
The meaning of the line of symmetry for a figure is explained in this section of Chapter 14 for Class 7. A form or figure is said to have symmetry when a line divides it into two identical parts. The line of symmetry is the line that divides the form. If there is a line around which the figure may be folded into two coinciding sections, the figure has a line of symmetry. The axis of symmetry is another name for the line of symmetry.
In nature, symmetry can be found in beehives, tree leaves, and flowers, among other things. Artists, manufacturers, designers, architects, and others use symmetrical designs.
Line of Symmetry for Regular Polygons:
A polygon is a closed figure made up entirely of line segments, as we all know. A triangle is a polygon with the smallest number of line segments. If all of the sides of a polygon are the same length and all of the angles are the same measure, it is said to be regular. A regular polygon is an equilateral triangle. A regular polygon is a square.
Because each of its sides is the same length and each of its angles is [Equation] an equilateral triangle is a regular polygon. As seen in the diagram below, an equilateral triangle has three lines of symmetry.
Because all of its sides are equal and each of its angles is a right angle, a square is also a regular polygon.
A square has four symmetry lines.
A regular polygon’s sides are all the same length, and each of its angles is[Equation]degrees. A pentagon has five symmetry lines.
All of the sides of a regular hexagon are equal, and each of the measures of the angles [Equation] degrees. Six lines of symmetry run through each of the vertices of a regular hexagon.
Note: When one half of a shape is the mirror image of the other, it is said to have a line of symmetry. As a result, line symmetry is intimately associated with mirror reflection.
Rotation Symmetry:
When an object rotates, its shape and dimensions remain unchanged. The rotation is centered on a fixed point. The center of rotation is the fixed place where the rotation happens. The angle of rotation refers to the angle at which the body rotates.
- A full turn is defined as a rotation of [Equation]degrees.
- A half-turn is equal to [Equation]rotations.
- A quarter-turn is a [Equation]rotation.
Rotational symmetry exists when a figure may be rotated less than [Equation]times around a point and still coincide with itself.
Line of Symmetry and Rotational Symmetry:
There are several shapes that exhibit both rotational and line symmetry.
Example:
(i) A square has line symmetry as well as rotational symmetry.
(ii) An equilateral triangle has both rotational and line symmetry.
(iii) A regular polygon has rotational as well as line symmetry.
FAQ:
What are the frequently asked questions in NCERT Solutions for Class 7 Maths Chapter 14 Symmetry?
The following are some of the most frequently asked questions about Chapter 14 Symmetry in NCERT Solutions for Class 7 Maths:
- Lines of symmetry for regular polygons
- Symmetry in rotation
- Rotational symmetry and line symmetry
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For the questions in NCERT Solutions for Class 7 Maths Chapter 14, INFINITY learns delivers the most exact answers. These solutions are available in PDF format and can be viewed online. The professionals explain the solutions to this chapter extremely clearly, with crisp graphics when necessary.
Is it vital to study NCERT Solutions for Class 7 Maths Chapter 14 for the exam?
Yes, all of the chapters in the NCERT Solutions for Class 7 Maths are crucial for both board exams and higher grades. To get good grades, students should practice all of the questions in NCERT Solutions for Class 7 Maths Chapter 14. It will assist students in grasping concepts and analyzing the types of questions that will be asked on the exam.
