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Olympiad Notes: Symmetry | Maths Olympiad Class 6 PDF Download
| Table of contents |
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| Introduction |
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| Linear Symmetry |
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| Line of Symmetry |
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| Reflection or Mirror Symmetry |
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| Three-dimensional shapes |
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| Net of a Solid |
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Introduction
Symmetry refers to the property of an object that allows it to be divided into two equal parts where one part perfectly aligns with the other.
Linear Symmetry
Linear symmetry is a specific type of symmetry involving the creation of a line through the centre of a figure. This line divides the figure into two identical parts, often referred to as mirror images or reflections of each other.In other words, one side of the figure corresponds exactly to the other side. The line responsible for this division is known as the line of symmetry or axis of symmetry.
A figure is considered asymmetrical when there is no line of symmetry which means it cannot be divided into two equal and matching halves.
Example of Linear Symmetry
Line of Symmetry
The "line of symmetry" is referred to as the "axis of symmetry" or "symmetry line," which is an imaginary line that divides a figure into two equal and mirror-image halves.
In regular polygons, the lines of symmetry correspond to the number of sides in the polygon.
A circle has an infinite number of lines of symmetry.
Reflection or Mirror Symmetry
Reflection or Mirror Symmetry is also known as mirror-image symmetry which occurs when a mirror is positioned along the central line of a figure. In this arrangement, the first half of the figure reflects through the mirror, creating an exact duplicate of the remaining half on the opposite side, equidistant from the mirror.
Three-dimensional shapes
Three-dimensional shapes (3-D shapes) are solid objects or figures characterized by having three dimensions: length, width and height. 3-D shapes include the cube, cuboid, cone, cylinder, sphere, prism and pyramid.
Net of a Solid
A geometry net is a two-dimensional shape that creates a three-dimensional solid when folded. To determine whether a given net can indeed form a solid, follow these steps:
Step 1: Start by ensuring that both the solid and the net have an identical number of faces. Additionally, make sure that the shapes of the solid's faces correspond to the shapes of the faces in the net.
Step 2: Proceed by mentally visualizing how the net should be folded to produce the solid. Confirm that all the sides of the net align and fit together correctly to create a solid shape.
Nets of Cube, Cuboid, Rectangular Prism, Pyramid, Cylinder and Cone are shown as:
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FAQs on Olympiad Notes: Symmetry - Maths Olympiad Class 6
| 1. What is linear symmetry and how is it observed in shapes? |  |
Ans. Linear symmetry, also known as reflection symmetry, is a type of symmetry where a shape can be divided into two identical halves that are mirror images of each other. This can be observed in various shapes, such as squares, rectangles, and triangles, where a line of symmetry can be drawn through the center, allowing each side to reflect the other perfectly.
| 2. What is a line of symmetry and can you give examples of shapes that have multiple lines of symmetry? | |
Ans. A line of symmetry is an imaginary line that divides a shape into two parts that are mirror images of each other. For instance, a square has four lines of symmetry, while an equilateral triangle has three. A circle has an infinite number of lines of symmetry because any diameter can be a line of symmetry.
| 3. What is reflection or mirror symmetry, and how does it differ from other types of symmetry? | |
Ans. Reflection or mirror symmetry occurs when one half of an object is a mirror image of the other half. This differs from rotational symmetry, where a shape can be rotated around a central point and still look the same. For example, a butterfly exhibits reflection symmetry, while a starfish shows both reflection symmetry and rotational symmetry.
| 4. How do three-dimensional shapes exhibit symmetry, and what are some examples? | |
Ans. Three-dimensional shapes can exhibit symmetry in various ways, such as having symmetrical faces or identical halves. Common examples include cubes, which have multiple planes of symmetry, and spheres, which have infinite lines of symmetry around their center. These symmetrical properties help in understanding their structure and design.
| 5. What is a net of a solid, and how does it relate to symmetry? | |
Ans. A net of a solid is a two-dimensional representation that shows all the faces of a three-dimensional shape laid out flat. It helps visualize how the solid can be constructed. The net can also exhibit symmetry; for example, the net of a cube shows symmetry in its square faces, demonstrating how they align when folded into a solid shape.
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Sep 23, 2025
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