# Important Questions Class 7 Mathematics Chapter 14

## Important Questions Class 7 Mathematics Chapter 14 – Symmetry

Mathematics is an important subject studied in school, but we need Mathematics to solve real-life problems, from daily expenses to large-scale constructions. This chapter discusses symmetry. Students have learned about symmetry in early classes.

In this chapter, students will learn about the various properties of symmetry as well as the mathematical applications of symmetry.

Symmetry is an important property in geometry. It has symmetry if an object can be divided into two equal halves. The line along which equal division occurs is called the axis of symmetry. Students must practise questions to score better in exams.

Extramarks is a leading company that provides students with all the important study materials. Our experts have collected the questions from different sources, such as the textbook exercises, CBSE sample papers, CBSE past years’ question papers, NCERT exemplar, and important reference books. They solved the questions so that students could follow the answers. Experienced professionals have further checked the answers to ensure the best quality of the content. Thus, the Important Questions Class 7 Mathematics Chapter 14 will help students  score better.

Extramarks is a leading company; we provide study materials related to CBSE and NCERT. You can download the study materials after registering on our official website. We provide CBSE syllabus, CBSE sample papers, CBSE past years’ question papers, CBSE revision notes, CBSE extra questions, NCERT books, NCERT solutions, NCERT important questions, NCERT Exemplars, vital formulas, and many more.

### Important Questions Class 7 Mathematics Chapter 14 – With Solutions

Extramarks is a leading company that provides all the important study materials related to CBSE and NCERT. Our experts have made this question series by collecting questions from different sources, such as the textbook exercises, CBSE sample papers, CBSE past years’ question papers, NCERT Exemplars, and important reference books. They have provided the solutions, and experienced professionals have further checked the answers to ensure the best quality of the content. Thus, the Important Questions Class 7 Mathematics Chapter 14 will help students  boost their preparation for their exams. The important questions are-

Question 1. What is symmetry? Explain briefly

Answer 1: Symmetry is defined as a geometrical concept, and any geometric shape can be symmetric or asymmetric. If an imaginary line passes through a shape and divides it into halves, and these halves overlap each other, then the shape is said to be symmetric. The two halves are equal and they overlap each other; if they do not overlap each other, then they are said to be asymmetric.

The imaginary line  is known as the line of symmetry.

Question 2. Enumerate the different types of symmetry?

Answer 2: The different types of symmetry are:

• Rotational symmetry
• Reflection symmetry
• Translation symmetry
• Glide reflection symmetry

Question 3. What do you understand by point symmetry?

Answer 3: Point symmetry refers to the existence of a central point or a position on an object.

Question 4. What is the other name given to the line of symmetry of an isosceles triangle?

Answer 4: The other name is median or altitude for the line of symmetry of an isosceles triangle.

In an isosceles triangle, any two sides are equal.

Question 5. Mention the other name given to the line of symmetry of a circle?

Answer 5: The other name for the line of symmetry of a circle is diameter.

Question 6. Enumerate three examples of shape which have no line of symmetry. Explain.

Answer 6: If in any figure, there is no line about which the figure may be folded and there is no possibility of coinciding in different parts of the mirror, then this means that the shape has no line of symmetry.

Such example could be:

• A scalene triangle.

In a scalene triangle, no two sides are equal.

• A parallelogram

Question 7. State the number of lines of symmetry indicated for the geometrical figures named below:

1. An equilateral triangle
2. An isosceles triangle
3. A scalene triangle
4. A square
5. A rectangle
6. A rhombus
7. A parallelogram
9. A regular hexagon
10. A circle
11. A regular pentagon

When the figures drawn below are folded along the dotted lines, the two parts on either side of the dotted lines coincide. This is one of  the important properties of geometrical figures and is called symmetry.

1. In an equilateral triangle, there are three sides, and all three sides are equal. There are three lines of symmetry in an equilateral triangle, as shown in the figure below:
1. In an isosceles triangle any two sides are equal as shown in the figure below:

An isosceles triangle has one line of symmetry.

1. In a scalene triangle, no two sides are equal as shown in the figure below. This type of triangle has no line of symmetry.
1. In a  square, there are four lines of symmetry as shown in the figure drawn below.
1. In a rectangle, there are two lines of symmetry present, as shown in the figure given below.
1. Two lines of symmetry are present in a rhombus, as shown in the figure given below. In a parallelogram, if all the sides are equal then it is a rhombus.
1. A parallelogram has no line of symmetry.
2. A quadrilateral has no line of symmetry.
3. A regular hexagon shape has six lines of symmetry as shown in the figure given below.
1. A circle has infinite lines of symmetry.
2. A regular pentagon shape has five lines of symmetry as shown in the figure given below.

Question 8. Give an example of the English letter or alphabet which has reflectional symmetry about a vertical mirror.

Reflective symmetry basically means symmetry related to mirror reflection. The English alphabets or letters which have reflective symmetry about a vertical mirror are A, H, I, M, O, U, V, W, X, Y.

Question 9. Identify the lines of symmetry in the following figures.

1. In the figure given above, it has three lines of symmetry.
2. In the figure given above, it has two lines of symmetry.
3. In the figure given above, it has three lines of symmetry.
4. In the figure given above, it has two lines of symmetry.
5. In the figure given above, it has four lines of symmetry.
6. In the figure given above, it has one line of symmetry.
7. In the figure given above, it has four lines of symmetry.
8. In the figure given above, it has six lines of symmetry.

Question 10. In the figures given below, the mirror line or the line of symmetry is presented as the dotted line. Identify the figure and complete it.

Answer 10: The line of symmetry has a concept which is similar to the reflection of a mirror. A mirror line aid in visualisation of the line of symmetry.

The figure obtained is a square.

The figure obtained is a triangle.

The figure obtained is a rhombus.

The figure obtained is a circle.

The figure obtained is a pentagon.

The figure obtained is an octagon.

Question 11. The different figures are given below. Which of the following figures has rotational symmetry of order more than 1? Add a note on rotational symmetry.

Answer 11: The movement of the clock is the best example of rotation. It is clockwise, otherwise, it is anti-clockwise. When the object is in rotation, there is no change in the shape or size of the object. Instead, the object rotates around a fixed point. The centre of rotation is the fixed point. The angle of turning is the angle of rotation. A 360-degree rotation means a full turn.

The answer to the above figures are given below:

1. The given figure has a rotational symmetry of 4.
2. The given figure has a rotational symmetry of 3
3. The given figure has a rotational symmetry of 1.
4. The given figure has a rotational symmetry of 2.
5. The given figure has a rotational symmetry of 3.
6. The given figure has a rotational symmetry of 4.

Question 12. The figures are given below. Give the order of rotational symmetry.

1. The above figure has rotational symmetry as 2.
2. The figure given above has rotational symmetry as 2.
3. The figure given above has rotational symmetry as 3.
4. The figure gives above has rotational symmetry as 4
5. The figure given above has rotational symmetry as 4.
6. The figure give above has rotational symmetry as 5.
7. The figure given above has rotational symmetry of 6.
8. The figure given above has rotational symmetry of 3.

Question 13. Draw and name the two figures which have both line symmetry and rotational symmetry.

Answer 13: Equilateral triangle has both lines of symmetry and rotational symmetry.

The line symmetry of the equilateral triangle is given below.

The rotational symmetry for an equilateral triangle is given below

Question 14. Name a triangle which has only one line of symmetry and has no rotational symmetry of order of more than 1.

The answer to the above question is an isosceles triangle.

The given above is an example of an isosceles triangle. In the triangle PQR, two sides namely PQ and PR are equal.

Question 15. Is it possible to draw a quadrilateral which does not have a line symmetry and is with a rotational symmetry of order of more than 1?

Answer 15: It is not possible to draw such a type of quadrilateral because a quadrilateral with a line symmetry may have rotational symmetry of order one but it is not more than one.

Question 16. Name a quadrilateral with line symmetry but not a rotational symmetry of order more than 1.

Answer 16: As shown in the description, it is a rhombus.

Question 17. Fill in the blanks.

 Shape Centre of rotation Order of rotation Angle of rotation Semi-circle Circle Regular hexagon Equilateral triangle Rhombus Rectangle Square

 Shape Centre of rotation Order of rotation Angle of rotation Semi-circle Mid-pointer of diameter is the centre of rotation. 1 360 degrees represent the angle of rotation. Circle Centre depicts the centre of rotation. Infinite Every angle represents the angle of rotation. Regular hexagon Intersecting point of diagonals is the centre of rotation. 6 60 degrees represent the angle of rotation. Equilateral triangle Intersecting points of media is the centre of rotation 3 120 degrees represent the angle of rotation. Rhombus Intersecting point of diagonals is the centre of rotation. 2 180 degrees represent the angle of rotation. Rectangle Intersecting point of diagonals is the centre of rotation. 2 180 degrees represent the angle of rotation. Square Intersecting point of diagonals is the centre of rotation. 4 90 degrees represent the angle of rotation.

Question 18. Name the quadrilaterals and mention with the help of diagram, which have both line symmetry and rotational symmetry of order more than 1.

Answer 18: As per the description, the square has both line symmetry and rotational symmetry of order more than 1.

Question 19. Answer the following question in yes or no.

• Can we have a rotational symmetry of order more than 1 when 45 degrees is the angle of rotation?
• Can we have a rotational symmetry of order more than 1 whose angle of rotation is 17 degrees?

1. Yes
2. No

Question 20. Why is symmetry important?

Answer 20: Shapes are part of our day-to-day lives. Some letters, like E, have only one line of symmetry. The letter S has only rotational symmetry, while the letter H has both  symmetries.

The study of symmetry is very important as it is encountered in our daily routine, and  the use of symmetry is also frequent in our daily lives.

The figures given above are the examples of rotational symmetry like fruit, wheel and road signs.

Question 21. Fill in the blanks:

• _________ leads to a symmetry in which the left-right orientation is very important and should be taken care of.
• Rotation turns the object around a ____________.
• The fixed point around which the rotation turns the object is known as _________
• ____________ is the angle at which the object rotates.
• A half-turn refers to rotation by _________
• A quarter-turn refers to rotation by __________
• The rotation could be either ______ or _________
• In   ____________ , complete rotation of 360 degrees, the number of times the object looks exactly the same.
• The order of symmetry of a square is ________
• The order of symmetry for an equilateral triangle is _______
• After a rotation, the object looks exactly the same and we say that the object has ________.
• Regular polygon has ______ lines of symmetry.
• Regular polygons have ____ sides and _____ angles.
• Regular polygons have ______ lines of symmetry.

1. Mirror reflection leads to a symmetry in which the left-right orientation is very important and should be taken care of.
2. Rotation turns the object around a fixed point.
3. The fixed point around which the rotation turns the object is known as centre of rotation.
4. Angle of rotation is the angle at which the object rotates.
5. A half-turn refers to rotation by 180 degrees.
6. A quarter-turn refers to rotation by 90 degrees
7. The rotation could be either clockwise or anticlockwise
8. In   order of rotational symmetry, complete rotation of 360 degrees, the number of times the object looks exactly the same.
9. The order of symmetry of a square is four.
10. The order of symmetry for an equilateral triangle is three.
11. After a rotation, the object looks exactly the same and we say that the object has rotational symmetry.
12. Regular polygon has many lines of symmetry.
13. Regular polygons have equal sides and equal angles.
14. Regular polygons have multiple lines of symmetry.

Question 22. Give a reason why the circle is the most symmetrical figure.

Answer 22: The circle is the most perfect symmetrical figure because of the following reasons:

• The circle has an unlimited number of lines of symmetry.
• The circle could be rotated around the centre through any angle.
• Every diameter or in other words every line through the centre forms a line of symmetry or reflectional symmetry.
• The circle has rotational symmetry around the centre for every angle.

Benefits of Solving Important Questions Class 7 Mathematics Chapter 14

Practice is very important for students. It helps them  generate interest in the subject matter and boost their confidence. Thus, the habit of solving questions will allow them to score better in exams. There will be multiple benefits to solving the questions compiled by the experts at Extramarks.TThe following are the advantages of answering Important Questions in Class 7 Mathematics Chapter 14:

• The textbook exercises need more questions, and students must seek help from other sources. It can be tough for them to collect questions from different books, and our experts have done the task for students. They have collated the questions from the textbook exercises, CBSE sample papers, CBSE past years’ question papers, NCERT Exemplars, and important reference books. So, students don’t have to search for questions in different books, but they will find them in Class 7 Mathematics Chapter 14 Important Questions. Thus, it will help them to practise more.
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• Many students fear mathematics because they have difficulty understanding the subject matter. Mathematics is an interesting subject; students will generate interest when they build confidence. Thus, practise helps students  develop their interests and therefore build confidence. Therefore, it boosts their preparation for the exams and thus helps them  get better marks. So, the Chapter 14 Class 7 Mathematics Important Questions will help them  build their interest in the subject matter.

Extramarks is a well-known company in India that provides all the important study materials related to CBSE and NCERT. One can download the study materials after registering on our official website. We provide CBSE syllabus, CBSE sample papers, CBSE extra questions, CBSE revision notes, CBSE past years’ question papers, NCERT books, NCERT solutions, NCERT important questions, NCERT exemplars, vital formulas and many more. Like the Important Questions Class 7 Mathematics Chapter 14, you will also find important questions for other chapters. Links to the study materials are given below-

• NCERT books
• Important questions
• CBSE Revision Notes
• CBSE syllabus
• CBSE sample papers
• CBSE past years’ question papers
• Important formulas
• CBSE extra questions