CBSE Class 7 > Class 7 Notes > Mathematics (Maths) (Old NCERT) > RD Sharma Solutions: Symmetry (Exercise 18.1)
RD Sharma Solutions: Symmetry (Exercise 18.1)
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Page 1
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 semi-circle
Solution:
(i) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore an equilateral triangle has 3 lines of symmetry.
(ii) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore an isosceles triangle has 1 line of symmetry.
(iii) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a scalene triangle has no line of symmetry.
(iv) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a rectangle has 2 lines of symmetry.
(v) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a rhombus has 2 lines of symmetry.
Page 2
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 semi-circle
Solution:
(i) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore an equilateral triangle has 3 lines of symmetry.
(ii) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore an isosceles triangle has 1 line of symmetry.
(iii) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a scalene triangle has no line of symmetry.
(iv) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a rectangle has 2 lines of symmetry.
(v) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a rhombus has 2 lines of symmetry.
(vi) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a square has 4 lines of symmetry.
(vii) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a parallelogram has no line of symmetry.
(viii) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a quadrilateral has no line of symmetry.
(ix) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a regular pentagon has 5 lines of symmetry.
(x) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a regular hexagon has 6 lines of symmetry.
(xi) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a circle has an infinite number of lines of symmetry all along the diameters.
(xii) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a semicircle has only one line of symmetry.
2. What other name can you give to the line of symmetry of
(i) An isosceles triangle?
(ii) A circle?
Solution:
(i) An isosceles triangle has only 1 line of symmetry. This line of symmetry is also known
as the altitude of an isosceles triangle.
Page 3
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 semi-circle
Solution:
(i) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore an equilateral triangle has 3 lines of symmetry.
(ii) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore an isosceles triangle has 1 line of symmetry.
(iii) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a scalene triangle has no line of symmetry.
(iv) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a rectangle has 2 lines of symmetry.
(v) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a rhombus has 2 lines of symmetry.
(vi) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a square has 4 lines of symmetry.
(vii) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a parallelogram has no line of symmetry.
(viii) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a quadrilateral has no line of symmetry.
(ix) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a regular pentagon has 5 lines of symmetry.
(x) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a regular hexagon has 6 lines of symmetry.
(xi) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a circle has an infinite number of lines of symmetry all along the diameters.
(xii) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a semicircle has only one line of symmetry.
2. What other name can you give to the line of symmetry of
(i) An isosceles triangle?
(ii) A circle?
Solution:
(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 infinite lines of symmetry all along its diameters.
3. Identify three examples of shapes with no line of symmetry.
Solution:
Page 4
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 semi-circle
Solution:
(i) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore an equilateral triangle has 3 lines of symmetry.
(ii) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore an isosceles triangle has 1 line of symmetry.
(iii) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a scalene triangle has no line of symmetry.
(iv) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a rectangle has 2 lines of symmetry.
(v) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a rhombus has 2 lines of symmetry.
(vi) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a square has 4 lines of symmetry.
(vii) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a parallelogram has no line of symmetry.
(viii) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a quadrilateral has no line of symmetry.
(ix) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a regular pentagon has 5 lines of symmetry.
(x) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a regular hexagon has 6 lines of symmetry.
(xi) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a circle has an infinite number of lines of symmetry all along the diameters.
(xii) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a semicircle has only one line of symmetry.
2. What other name can you give to the line of symmetry of
(i) An isosceles triangle?
(ii) A circle?
Solution:
(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 infinite lines of symmetry all along its diameters.
3. Identify three examples of shapes with no line of symmetry.
Solution:
A scalene triangle, a parallelogram and a trapezium do not have any line of symmetry.
4. Identify multiple lines of symmetry, if any, in each of the following figures:
Solution:
(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.
Page 5
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 semi-circle
Solution:
(i) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore an equilateral triangle has 3 lines of symmetry.
(ii) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore an isosceles triangle has 1 line of symmetry.
(iii) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a scalene triangle has no line of symmetry.
(iv) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a rectangle has 2 lines of symmetry.
(v) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a rhombus has 2 lines of symmetry.
(vi) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a square has 4 lines of symmetry.
(vii) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a parallelogram has no line of symmetry.
(viii) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a quadrilateral has no line of symmetry.
(ix) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a regular pentagon has 5 lines of symmetry.
(x) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a regular hexagon has 6 lines of symmetry.
(xi) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a circle has an infinite number of lines of symmetry all along the diameters.
(xii) If a line divides a figure into two parts such that when the figure is folded about the
line the two parts of the figure coincide, then the line is known as the line of symmetry.
Therefore a semicircle has only one line of symmetry.
2. What other name can you give to the line of symmetry of
(i) An isosceles triangle?
(ii) A circle?
Solution:
(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 infinite lines of symmetry all along its diameters.
3. Identify three examples of shapes with no line of symmetry.
Solution:
A scalene triangle, a parallelogram and a trapezium do not have any line of symmetry.
4. Identify multiple lines of symmetry, if any, in each of the following figures:
Solution:
(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.
Read MoreFAQs on RD Sharma Solutions: Symmetry (Exercise 18.1)
| 1. What exactly is a line of symmetry and how do I identify it in different shapes? |  |
Ans. A line of symmetry divides a shape into two identical halves that mirror each other perfectly. To identify it, fold the shape mentally or physically along a line-if both sides match exactly, it's a line of symmetry. Rectangles have two, squares have four, and circles have infinite lines of symmetry. Practice with geometric shapes to recognise symmetrical patterns quickly.
| 2. How many lines of symmetry does a regular polygon have, and why? | |
Ans. A regular polygon has as many lines of symmetry as it has sides. A regular triangle has three lines, a square has four, and a regular pentagon has five. This occurs because each line passes through a vertex and the midpoint of the opposite side (or through two opposite vertices), creating perfect mirror images. Understanding this relationship helps solve Exercise 18.1 problems efficiently.
| 3. Why don't all shapes have the same number of lines of symmetry? | |
Ans. Different shapes possess varying symmetry based on their structure and angles. Regular shapes with equal sides and angles have multiple symmetric lines, whilst irregular shapes may have none or just one. An isosceles triangle has one line of symmetry, but an equilateral triangle has three. Shape properties determine symmetrical possibilities-this foundational concept underpins CBSE Class 7 symmetry exercises.
| 4. What's the difference between a shape with one line of symmetry and one with no symmetry? | |
Ans. A shape with one line of symmetry can be folded along that single line so both halves match perfectly; examples include isosceles triangles and kites. A shape with no symmetry cannot be divided this way-no fold produces identical halves. Recognising this distinction is crucial for solving symmetry problems in NCERT Class 7 Mathematics, especially in identifying asymmetrical figures during assessments.
| 5. How do I check if a shape has rotational symmetry, and is it different from line symmetry? | |
Ans. Rotational symmetry means a shape looks identical when rotated around a central point by less than 360°. Line symmetry involves folding along a straight line. A square has both: four lines of symmetry and rotational symmetry of order four. These are distinct properties-a shape can have one without the other. Use flashcards and mind maps to differentiate between these symmetry types effectively.
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