Symmetry and Visualising Solid Shapes for Class 7

Table of Content

The study of symmetry and visualizing solid shapes is an essential aspect of geometry that offers unique insights into the order and aesthetics of the world around us. These concepts play a fundamental role in various fields from art and design to architecture. In this chapter, we will delve into the fascinating world of symmetry and solid shapes by exploring their significance and applications.

  • Symmetry
  • Linear Symmetry
  • Reflection or Mirror Symmetry
  • Visualising Solid Shapes
  • Three-dimensional Shapes
  • Symmetry

    Symmetry is a concept that revolves around the balance and proportion of objects. When two shapes are identical in both shape and size, they are considered to be symmetrical. Symmetry can be found in nature, art and man-made designs.

    Examples of Symmetry in Nature

    Linear Symmetry

    This particular symmetry type involves drawing a line through the centre of a shape.

    When a line is drawn in a way that splits the figure into two perfectly matching halves where the left side mirrors the right side, the figure is said to have line symmetry. This dividing line is referred to as the Line of Symmetry or Axis of Symmetry.

    If there is no line that can divide this balance, the figure is considered asymmetrical.

    Linear Symmetry and Asymmetry in Trees

    Alphabets H and X have lines of symmetry. Therefore, they are symmetrical.

    Symmetrical Letters H and X

    Alphabets N and P have no line of symmetry. Therefore, they are asymmetrical.

    Asymmetrical Objects: Letters N and P

    Examples of Linear Symmetry:

    Linear Symmetry Examples in Shapes and Letters

    Line of Symmetry in Plane Figures:

    Lines of Symmetry in Geometric Shapes

    Regular polygons have lines of symmetry equal to the number of their sides.

    Regular Polygons with Diagonals Illustration

    A circle has an infinite number of lines of symmetry.

    Electric Dipole and Ring Field Lines

    Reflection or Mirror Symmetry

    Reflection symmetry occurs when one half of a figure reflects through a central line (a mirror), creating an identical half on the opposite side at the same distance. It is also known as mirror symmetry. Examples of reflection symmetry are as follows:

    Reflection or Mirror Symmetry Examples

    Visualising Solid Shapes

    Visualising solid shapes is a part of geometry that involves the understanding and manipulation of three-dimensional objects. This is to visualise, identify and work with various solid shapes in three-dimensional space.

    Three-dimensional Shapes

    A three-dimensional shape is a solid object characterized by having three dimensions: length, breadth (width) and height. Here are the properties of some common three-dimensional shapes:

    Cube: A cube features 12 edges, 6 faces and 8 vertices.

    Cubes and Cube-based Structures Comparison

    Cuboid: A cuboid also possesses 12 edges, 6 faces and 8 vertices.

    Shapes: Cuboid and Brick Examples

    Cylinder: A cylinder exhibits 2 edges, 3 faces and no vertices.

    Cylinder in Geometry and Everyday Objects

    Cone: A cone displays 1 edge, 2 faces and 1 vertex.

    Cone Shapes and Real-life Example

    Sphere: A sphere has 0 edges, 1 face and 0 vertices.

    Sphere and Ball Geometry Illustration

    Pyramid: A pyramid is a geometric shape made by joining a polygonal base to a single point called the apex. The edges connecting the base to the apex create triangular faces known as lateral faces.

    3D Pyramid Structure Diagram

    A triangular pyramid is a pyramid with a triangular base. It has 4 faces, 4 vertices and 6 edges in its structure. It is also known as a tetrahedron,

    Pyramidal Shape and Puzzle Comparison

    Prism: A prism is a three-dimensional object that has two identical ends. The ends of the prism can take the shape of a triangle, square, rectangle or any other polygon with n sides while the sides connecting these ends are typically in the form of rectangles or parallelograms. The name of the prism is determined by the shape of its base.

    Types of Prisms in Geometry

    A triangular prism is a polyhedron constructed from two triangular bases and three rectangular sides. This particular prism exhibits 5 faces, 6 vertices and 9 edges within its structure.

    Triangular Prism and Tent Comparison

    Quick Video Recap

    In this section, you will find interesting and well-explained topic-wise video summary of the topic, perfect for quick revision before your Olympiad exams.

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