All questions of Symmetry for Class 6 Exam

Understanding Rotational Symmetry
Rotational symmetry is a property of a shape that allows it to look the same after a certain amount of rotation about a central point. In simpler terms, if you can rotate a figure and it looks identical at some angle less than 360 degrees, it has rotational symmetry.
Analysis of the Given Figures
1. Equilateral Triangle
- An equilateral triangle has three equal sides and angles.
- It has rotational symmetry at 120 degrees (360/3), meaning it looks the same after a rotation of 120 degrees.
2. Rectangle
- A rectangle has opposite sides equal and all angles right angles.
- It has rotational symmetry at 180 degrees (360/2), so it appears the same when rotated halfway around.
3. Circle
- A circle has infinite lines of symmetry and can be rotated about its center by any angle, maintaining its appearance.
- Hence, it has an infinite degree of rotational symmetry.
4. Scalene Triangle
- A scalene triangle has all sides and angles different.
- When rotated, it does not align with its original position at any angle other than 360 degrees.
Conclusion
The correct answer is option 'D', the scalene triangle, as it does not have any rotational symmetry. Unlike the other shapes, it cannot be rotated to look the same at any angle less than 360 degrees.

Understanding Rotation Symmetry
In geometry, rotation symmetry refers to how a shape looks after being turned around a central point. For a shape to look the same after being rotated 180 degrees, it must have a specific symmetry.
Evaluating Each Option

• Option A: Letters like F, L, P, R
  
  • These letters do not maintain their appearance when rotated 180 degrees.
  
  
• Option B: Equilateral Triangle
  
  • When an equilateral triangle is rotated 180 degrees, it still looks the same. This is because all sides and angles are equal, allowing for rotational symmetry.
  
  
• Option C: Numbers like 4, 5, 6
  
  • These numbers change their appearance when rotated 180 degrees. For example, the number 5 becomes unrecognizable and the number 6 looks like a 9.
  
  
• Option D: None of the above
  
  • This option is incorrect since the equilateral triangle does have the desired rotational symmetry.
  
  

Conclusion
The correct answer is option B, the equilateral triangle. Its symmetrical properties allow it to remain unchanged when rotated 180 degrees, making it a perfect example of rotational symmetry. The other options lack this characteristic, confirming that only the equilateral triangle fits the criteria.

The smallest angle of rotation that maps a regular hexagon onto itself is 60 degrees, corresponding to its order of rotational symmetry.

A square has rotational symmetry at 90 degrees, which means it looks the same after a 90-degree rotation.

A parallelogram has rotational symmetry at 180 degrees but does not have any lines of symmetry because its sides are not equal.

Understanding Lines of Symmetry
Lines of symmetry are imaginary lines that divide a shape into two identical halves, such that one half is a mirror image of the other.
Characteristics of a Rhombus
- A rhombus is a type of quadrilateral where all four sides are of equal length.
- The opposite angles of a rhombus are equal, and adjacent angles are supplementary.
Lines of Symmetry in a Rhombus
A rhombus has two lines of symmetry:
- Diagonal Symmetries: The two diagonals of the rhombus serve as lines of symmetry.
- When you draw a diagonal, it divides the rhombus into two congruent triangles.
- Each triangle is a mirror image of the other.
- Identifying the Diagonals:
- One diagonal runs from one vertex to the opposite vertex.
- The second diagonal crosses the first and runs from the other two vertices.
Visualizing the Symmetry
- If you fold the rhombus along either of its diagonals, the two halves will align perfectly.
- This property shows that there are indeed two lines of symmetry in a rhombus.
Conclusion
In conclusion, the correct answer to the question regarding the number of lines of symmetry in a rhombus is option 'C', which states that there are 2 lines of symmetry. Understanding this concept is essential in geometry, especially when studying polygons and their properties.

Understanding Lines of Symmetry
Lines of symmetry are imaginary lines that divide a shape into two identical halves. If you can fold a shape along a line and both halves match perfectly, that line is a line of symmetry.
Equilateral Triangle Characteristics
- An equilateral triangle has three equal sides and three equal angles (each measuring 60 degrees).
- This symmetry makes it unique among triangles.
Identifying Lines of Symmetry
1. Vertex to Opposite Side:
- Each line of symmetry in an equilateral triangle can be drawn from a vertex to the midpoint of the opposite side.
- This line splits the triangle into two equal halves.
2. Total Lines of Symmetry:
- Since there are three vertices, you can draw three distinct lines of symmetry.
- Each line corresponds to one of the triangle's vertices.
Conclusion
- Therefore, an equilateral triangle has 3 lines of symmetry.
- This is why the correct answer is option 'C'.
Understanding symmetry helps in recognizing patterns in geometry, making it an essential concept in mathematics.

A regular pentagon has rotational symmetry at 72 degrees, so it looks the same after a 72-degree rotation.

Lines of Symmetry in a Square
The correct answer is option 'C', which is 4 lines of symmetry for a square. Let's delve into the explanation below:

Definition of Symmetry
Symmetry is a concept in geometry that refers to a shape or object that can be divided into two or more identical parts that mirror each other. Lines of symmetry are imaginary lines that divide a shape into two symmetrical halves.

Symmetry in a Square
- A square is a four-sided polygon with all sides equal in length and all angles equal to 90 degrees.
- A square has 4 lines of symmetry, which means it can be divided into 4 equal parts that are symmetrical to each other.
- The lines of symmetry in a square run through the midpoint of each side and intersect at the center of the square, forming right angles.

Explanation of 4 Lines of Symmetry
- The first line of symmetry runs horizontally across the middle of the square, dividing it into two equal halves.
- The second line of symmetry runs vertically from top to bottom, also dividing the square into two symmetrical parts.
- The third line of symmetry runs diagonally from the top left corner to the bottom right corner, creating two more symmetrical sections.
- The fourth line of symmetry runs diagonally from the top right corner to the bottom left corner, completing the 4 lines of symmetry in a square.

Conclusion
In conclusion, a square has 4 lines of symmetry due to its symmetrical properties, making it a shape with equal halves when divided along these lines.

When you fold a kite shape along its line of symmetry:
- The two halves overlap perfectly: When you fold a kite shape along its line of symmetry, the two halves will perfectly overlap each other. This is because a kite shape has a line of symmetry that divides it into two equal halves that are mirror images of each other. So, when you fold the kite along this line, the two halves will fit perfectly on top of each other.
- This is similar to folding a piece of paper in half along its center crease. The two halves of the paper will align perfectly, creating a mirror image of each other.
- Importance of symmetry: Symmetry is an important concept in mathematics and geometry. It helps us understand patterns, shapes, and structures in a more organized and systematic way. Folding a shape along its line of symmetry is one way to demonstrate this concept visually.
- Visual representation: To better understand this concept, you can try drawing a kite shape on a piece of paper and folding it along its line of symmetry. You will see that the two halves overlap perfectly, showing the symmetry of the shape.
- Conclusion: Folding a kite shape along its line of symmetry results in the two halves overlapping perfectly. This demonstrates the concept of symmetry and helps us visualize the mirror image relationship between the two halves of the shape.

A regular hexagon has 6 lines of symmetry, each line passing through opposite vertices or midpoints of opposite sides.

A circle has an infinite number of lines of symmetry, so folding along any diameter will cause the two halves to overlap perfectly.

An isosceles triangle has only one line of symmetry that passes through its vertex and the midpoint of the base.

A scalene triangle has no lines of symmetry because all its sides and angles are different.

A square looks the same after being rotated by 90 degrees because it has rotational symmetry at this angle.

The order of rotational symmetry of a regular pentagon is 5, meaning it can be rotated by 72°, 144°, 216°, 288°, and 360° to look the same.

A regular octagon has 8 lines of symmetry, one for each vertex and the midpoint of the opposite side.