Symmetry and Visualising Solid Shapes

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

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.

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.

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

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

Examples of Linear Symmetry:

Line of Symmetry in Plane Figures:

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

A circle has an infinite number of lines of symmetry.

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:

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.

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

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

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

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

⇒ 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.

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,

⇒ 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.

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.