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Everyday Mathematics: Symmetry | Maths Olympiad Class 6 PDF Download
Q1: Which of the following letters has only one line of symmetry?
a) A
b) H
c) X
d) O
Ans: a) A
Explanation:
A has only 1 vertical line of symmetry. H has 2 (vertical and horizontal), X has 2 diagonal lines, and O has infinite lines of symmetry.
Q2: Which of the following shapes has no line of symmetry?
a) Rectangle
b) Equilateral triangle
c) Scalene triangle
d) Square
Ans: c) Scalene triangle
Explanation:
A scalene triangle has no equal sides or angles, so it has no line of symmetry. The others have at least one.
Q3: A square has how many lines of symmetry?
a) 2
b) 4
c) 6
d) 8
Ans: b) 4
Explanation:
A square has 4 lines of symmetry: 2 diagonals and 2 midlines (horizontal and vertical).
Q4: Which of the following objects is most likely to have rotational symmetry?
a) A leaf
b) A clock
c) A brick
d) A pencil
Ans: b) A clock
Explanation:
A clock can be rotated by multiples of 30° and look the same, giving it rotational symmetry of order 12.
Q5: Which shape has exactly two lines of symmetry that are vertical and horizontal?
a) Rectangle
b) Rhombus
c) Equilateral triangle
d) Circle
Ans: a) Rectangle
Explanation:
A rectangle has exactly two lines of symmetry — one vertical and one horizontal.
A rhombus has two lines of symmetry, but these are along the diagonals, not vertical/horizontal.
Q6: Which of the following figures has infinite lines of symmetry?
a) Triangle
b) Square
c) Circle
d) Pentagon
Ans: c) Circle
Explanation:
A circle can be folded along any diameter and still match perfectly, so it has infinite lines of symmetry.
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FAQs on Everyday Mathematics: Symmetry - Maths Olympiad Class 6
| 1. What is symmetry in mathematics? |  |
Ans. Symmetry in mathematics refers to a situation where a shape or object can be divided into two or more identical parts that are arranged in a balanced and proportionate way. This can occur in various forms such as reflective symmetry, rotational symmetry, and translational symmetry. Reflective symmetry involves a mirror line where one side is a mirror image of the other, while rotational symmetry occurs when a shape can be rotated around a central point and still look the same.
| 2. How can we identify lines of symmetry in shapes? | |
Ans. To identify lines of symmetry in shapes, one can fold the shape along a potential line and check if both halves match perfectly. For simple shapes like squares or circles, lines of symmetry can be easily visualized. More complex shapes may require careful observation, but generally, a shape can have multiple lines of symmetry, such as a butterfly having two lines of symmetry.
| 3. What are some real-life examples of symmetry? | |
Ans. Real-life examples of symmetry include the human face, which often exhibits bilateral symmetry, the wings of butterflies, which are symmetrical in design, and architectural structures like bridges and buildings that often use symmetrical designs for aesthetic appeal and structural integrity. Nature also showcases symmetry in flowers and leaves.
| 4. Why is understanding symmetry important in mathematics? | |
Ans. Understanding symmetry is important in mathematics because it helps in recognizing patterns and relationships between shapes. It plays a crucial role in geometry and is fundamental in various fields such as art, architecture, and physics. Symmetry can simplify complex problems and is essential for the study of transformations and congruence in shapes.
| 5. How can symmetry be applied in art and design? | |
Ans. Symmetry is widely applied in art and design to create visually appealing compositions. Artists often use symmetrical designs to create balance and harmony within their work. In graphic design, symmetry can enhance the aesthetic quality of logos and layouts, making them more memorable and effective. Additionally, symmetrical patterns are prevalent in textiles, architecture, and nature-inspired designs.
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