Class 7 Exam > Class 7 Notes > RD Sharma Solutions for Class 7 Mathematics > RD Sharma Solutions - Ex-18.1, Symmetry, Class 7, Math
Ex-18.1, Symmetry, Class 7, Math RD Sharma Solutions | RD Sharma Solutions for Class 7 Mathematics PDF Download
Question 1:
State the number of lines of symmetry for the following figures:
(i) An equilateral triangle
(ii) An isosceles triangle
(iii) A scalene triangle
(iv) A rectangle
(v) A rhombus
(vi) A square
(vii) A parallelogram
(viii) A quadrilateral
(ix) A regular pentagon
(x) A regular hexagon
(xi) A circle
(xii) A semicircle
Answer 1:
(i) An equilateral triangle has 3 lines of symmetry.
(ii) An isosceles triangle has 1 line of symmetry.
(iii) A scalene triangle has no line of symmetry.
(iv) A rectangle has 2 lines of symmetry.
(v) A rhombus has 2 lines of symmetry.
(vi) A square has 4 lines of symmetry.
(vii) A parallelogram has no line of symmetry.
(viii) A quadrilateral has no line of symmetry.
(ix) A regular pentagon has 5 lines of symmetry.
(x) A regular hexagon has 6 lines of symmetry.
(xi) A circle has an infinite number of lines of symmetry all along the diameters.
(xii) A semicircle has only one line of symmetry.
Question 2:
What other name can you give to the line of symmetry of
(i) An isosceles triangle?
(ii) A circle?
Answer 2:
(i) An isosceles triangle has only 1 line of symmetry.
This line of symmetry is also known as the altitude of an isosceles triangle.
(ii) A circle has an infinite number of lines of symmetry all along its diameters.
Question 3:
Identify three examples of shapes with no line of symmetry.
Answer 3:
A scalene triangle, a parallelogram and a trapezium do not have any line of symmetry.
Question 4:
Identify multiple lines of symmetry, if any, in each of the following figures:
Answer 4:
(A) The given figure has 3 lines of symmetry. Therefore it has multiple lines of symmetry.
(B) The given figure has 2 lines of symmetry. Therefore it has multiple lines of symmetry.
(C) The given figure has 3 lines of symmetry. Therefore it has multiple lines of symmetry.
(D) The given figure has 2 lines of symmetry. Therefore it has multiple lines of symmetry.
(E) The given figure has 4 lines of symmetry. Therefore it has multiple lines of symmetry.
(F) The given figure has only 1 line of symmetry.
(G) The given figure has 4 lines of symmetry. Therefore it has multiple lines of symmetry.
(H) The given figure has 6 lines of symmetry. Therefore it has multiple lines of symmetry.
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FAQs on Ex-18.1, Symmetry, Class 7, Math RD Sharma Solutions - RD Sharma Solutions for Class 7 Mathematics
| 1. What is symmetry in mathematics? |  |
Ans. Symmetry in mathematics is a concept that refers to a perfect balance or similarity in shape, size, and arrangement of objects or figures when they are divided into equal parts and one part is the mirror image of the other.
| 2. How is symmetry useful in real life? | |
Ans. Symmetry is useful in real life in various ways. For example, it is used in architecture to create visually appealing buildings and structures. It is also used in design and art to create balance and harmony. In nature, symmetry can be seen in the arrangement of petals in flowers, the shapes of leaves, and the patterns on butterfly wings.
| 3. How can we determine if a figure has symmetry? | |
Ans. To determine if a figure has symmetry, we can use the method of folding. If a figure can be folded along a line such that the two halves match exactly, then the figure has symmetry. Another way is to observe if a figure has rotational symmetry, which means it can be rotated by a certain angle and still look the same.
| 4. What are the different types of symmetry? | |
Ans. There are three main types of symmetry - reflectional symmetry, rotational symmetry, and translational symmetry. Reflectional symmetry is when a figure can be divided into two equal halves that are mirror images of each other. Rotational symmetry is when a figure can be rotated by a certain angle and still look the same. Translational symmetry is when a figure can be shifted or translated without changing its shape.
| 5. How is symmetry related to patterns? | |
Ans. Symmetry plays a significant role in creating and identifying patterns. Patterns often exhibit symmetry, whether it is in the arrangement of colors, shapes, or designs. Symmetry helps in creating balance and repetition, making patterns visually appealing and harmonious. Additionally, recognizing symmetry in patterns can aid in predicting and extending the pattern.
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