RD Sharma Solutions Class 7 Chapter 18 Symmetry

Read RD Sharma Solutions Class 7 Chapter 18 Symmetry below, students should study RD Sharma class 7 Mathematics available on Studiestoday.com with solved questions and answers. These chapter wise answers for class 7 Mathematics have been prepared by teacher of Grade 7. These RD Sharma class 7 Solutions have been designed as per the latest NCERT syllabus for class 7 and if practiced thoroughly can help you to score good marks in standard 7 Mathematics class tests and examinations

Exercise 18.1

 

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 semi-circle 

Solution 1:

(i) An equilateral triangle:

The line of symmetry splits a figure into two parts in such a way that when the figure is folded along the line, the two parts of the figure overlap.

As a result, an equilateral triangle has three symmetry lines.

 

(ii) An isosceles triangle:

The line of symmetry splits a figure into two parts in such a way that when the figure is folded along the line, the two parts of the figure overlap.

As a result, an isosceles triangle has only one symmetry axis.

 

(iii) A scalene triangle:

The line of symmetry splits a figure into two parts in such a way that when the figure is folded along the line, the two parts of the figure overlap.

As a result, a scalene triangle has no symmetry rows.

 

(iv) A rectangle:

The line of symmetry splits a figure into two parts in such a way that when the figure is folded along the line, the two parts of the figure overlap.

As a result, a rectangle has two symmetry lines.

 

(v) A rhombus:

The line of symmetry splits a figure into two parts in such a way that when the figure is folded along the line, the two parts of the figure overlap.

As a result, a rhombus has two symmetry lines.

 

(vi) A square:

The line of symmetry splits a figure into two parts in such a way that when the figure is folded along the line, the two parts of the figure overlap.

As a result, a square has four symmetry lines.

 

(vii) A parallelogram:

The line of symmetry splits a figure into two parts in such a way that when the figure is folded along the line, the two parts of the figure overlap.

As a result, a parallelogram has no symmetry rows.

 

(viii) A quadrilateral:

The line of symmetry splits a figure into two parts in such a way that when the figure is folded along the line, the two parts of the figure overlap.

As a result, a quadrilateral has no symmetry rows.

 

(ix) A regular pentagon:

A regular pentagon The line of symmetry splits a figure into two parts in such a way that when the figure is folded along the line, the two parts of the figure overlap.

As a result, a regular pentagon has five symmetry lines.

 

(x) A regular hexagon:

The line of symmetry splits a figure into two parts in such a way that when the figure is folded along the line, the two parts of the figure overlap.

As a result, a regular hexagon has six symmetry lines.

 

(xi) A circle:

The line of symmetry splits a figure into two parts in such a way that when the figure is folded along the line, the two parts of the figure overlap.

As a result, a circle has an infinite number of symmetry lines running around its diameters.

 

(xii) A semi-circle:

The line of symmetry splits a figure into two parts in such a way that when the figure is folded along the line, the two parts of the figure overlap.

As a result, a semicircle has only one symmetry axis.

 

Question :2. What other name can you give to the line of symmetry of

(i) An isosceles triangle?

(ii) A circle? 

Solution 2:

(i) There is just one symmetry line in an isosceles triangle. The altitude of an isosceles triangle is also known as this symmetry axis.

RD Sharma Solutions Class 7 Chapter 18 Symmetry

(ii) A circle has infinite symmetry lines running the length of its diameters.

RD Sharma Solutions Class 7 Chapter 18 Symmetry

 

Question :3. Identify three examples of shapes with no line of symmetry. 

Solution 3:

RD Sharma Solutions Class 7 Chapter 18 Symmetry

There is no symmetry line in a scalene triangle, a parallelogram, or a trapezium.

 

Question :4. Identify multiple lines of symmetry, if any, in each of the following figures:

RD Sharma Solutions Class 7 Chapter 18 Symmetry

Solution 4:

 

(a) There are three symmetry lines in the specified figure. As a result, it has several symmetry lines.

RD Sharma Solutions Class 7 Chapter 18 Symmetry

 

(b) There are two symmetry lines in the specified diagram. As a result, it has several symmetry lines.

RD Sharma Solutions Class 7 Chapter 18 Symmetry

(c) There are three symmetry lines in the specified figure. As a result, it has several symmetry lines.

RD Sharma Solutions Class 7 Chapter 18 Symmetry

(d) There are two symmetry lines in the specified diagram. As a result, it has several symmetry lines.

RD Sharma Solutions Class 7 Chapter 18 Symmetry

(e) There are four symmetry lines in the specified figure. As a result, it has several symmetry lines.

RD Sharma Solutions Class 7 Chapter 18 Symmetry

(f) There is only one symmetry line in the given figure.

RD Sharma Solutions Class 7 Chapter 18 Symmetry

(g) There are four symmetry lines in the specified figure. As a result, it has several symmetry lines.

RD Sharma Solutions Class 7 Chapter 18 Symmetry

(h) There are six symmetry lines in the specified figure. As a result, it has several symmetry lines.

RD Sharma Solutions Class 7 Chapter 18 Symmetry

 

Exercise 18.2

 

Question :1. In the following figures, the mirror line (i.e. the line of symmetry) is given as dotted line. Complete each figure performing reflection in the dotted (mirror) line. Also, try to recall name of the complete figure.

RD Sharma Solutions Class 7 Chapter 18 Symmetry


Solution 1: 

(a) It will be in the form of a rectangle.

RD Sharma Solutions Class 7 Chapter 18 Symmetry

(b) It will be in the form of a triangle.

RD Sharma Solutions Class 7 Chapter 18 Symmetry

(c) It will be in the form of a rhombus.

RD Sharma Solutions Class 7 Chapter 18 Symmetry

(d) It will be in the form of a circle.

RD Sharma Solutions Class 7 Chapter 18 Symmetry

(e) It will be in the form of a pentagon.

RD Sharma Solutions Class 7 Chapter 18 Symmetry

(f) It will be in the form of an octagon.

 RD Sharma Solutions Class 7 Chapter 18 Symmetry

 

Question :2. Each of the following figures shows paper cuttings with punched holes. Copy these figures on a plane sheet and mark the axis of symmetry so that if the paper is folded along it, then the wholes on one side of it coincide with the holes on the other side.

RD Sharma Solutions Class 7 Chapter 18 Symmetry


Solution  2:

The lines of symmetry in the given figures are as follows:

RD Sharma Solutions Class 7 Chapter 18 Symmetry

 

Question :3. In the following figures if the dotted lines represent the lines of symmetry, find the other hole(s).

RD Sharma Solutions Class 7 Chapter 18 Symmetry

Solution 3: 

The following are the other holes in the figure:

RD Sharma Solutions Class 7 Chapter 18 Symmetry 

 

Exercise 18.3 


Question :1. Give the order of rotational symmetry for each of the following figures when rotated about the marked point (x):

RD Sharma Solutions Class 7 Chapter 18 Symmetry

Solution 1:

(i) When a figure fits into itself more than once during a complete 360o rotation, it is said to have rotational symmetry.

As a result, the rotational symmetry of the given figure is 4.

 

(ii) When a figure fits into itself more than once during a complete 360o rotation, it is said to have rotational symmetry.

As a result, the rotational symmetry of the given figure is 3.

 

(iii) If a figure fits into itself more than once during a complete rotation of 360o, it is said to have rotational symmetry.

As a result, the rotational symmetry of the given figure is equal to three.

 

(iv) When a figure fits into itself more than once during a complete 360o rotation, it is said to have rotational symmetry.

As a result, the rotational symmetry of the given figure is 4.

 

(v) When a figure fits into itself more than once during a complete 360o rotation, it is said to have rotational symmetry.

As a result, the rotational symmetry of the given figure is 2.

 

(vi) When a figure fits into itself more than once during a complete 360o rotation, it is said to have rotational symmetry.

As a result, the rotational symmetry of the given figure is 4.

 

(vii) If a figure fits into itself more than once during a complete rotation of 360o, it is said to have rotational symmetry.

As a result, the rotational symmetry of the given figure is equal to four.

 

(viii) When a figure fits into itself more than once during a complete 360o rotation, it is said to have rotational symmetry.

As a result, the rotational symmetry of the given figure is 6.

 

(ix) When a figure fits into itself more than once during a complete 360o rotation, it is said to have rotational symmetry.

As a result, the rotational symmetry of the given figure is 3.

 

Question :2. Name any two figures that have both line symmetry and rotational symmetry. 

Solution 2:

Both lines of symmetry and rotational symmetry exist in an equilateral triangle and a square.

RD Sharma Solutions Class 7 Chapter 18 Symmetry

 

 

Question :3. Give an example of a figure that has a line of symmetry but does not have rotational symmetry. 

Solution  3:

A line of symmetry exists in a semicircle and an isosceles triangle, but rotational symmetry does not exist.

 RD Sharma Solutions Class 7 Chapter 18 Symmetry

 

 

Question :4. Give an example of a geometrical figure which has neither a line of symmetry nor a rotational symmetry. 

Solution  4:

There is no line of symmetry or rotational symmetry in a scalene triangle.

RD Sharma Solutions Class 7 Chapter 18 Symmetry

 

 

Question :5. Give an example of a letter of the English alphabet which has

(i) No line of symmetry

(ii) Rotational symmetry of order 2. 

Solution 5:

(i) No line of symmetry:

Z is the only letter in the English alphabet that does not have a symmetry line. 

(ii) Rotational symmetry of order 2:

The letter N is the only letter in the English alphabet with rotational symmetry of order two.

 

Question :6. What is the line of symmetry of a semi-circle? Does it have rotational symmetry? 

Solution  6:

There is just one symmetry line in a semicircle (half of a circle). There is just one symmetry line in the illustration. Along the perpendicular bisector I of the diameter XY, the figure is symmetric. There is no rotational symmetry in a semi-circle.

 RD Sharma Solutions Class 7 Chapter 18 Symmetry

 

 

Question :7. Draw, whenever possible, a rough sketch of

(i) a triangle with both line and rotational symmetries.

(ii) a triangle with only line symmetry and no rotational symmetry.

(iii) a quadrilateral with a rotational symmetry but not a line of symmetry.

(iv) a quadrilateral with line symmetry but not a rotational symmetry. 

Solution 7:

(i) An equilateral triangle has three lines of symmetry and order three rotational symmetry.

RD Sharma Solutions Class 7 Chapter 18 Symmetry

(ii) There is just one line of symmetry in an isosceles triangle, and there is no rotational symmetry.

RD Sharma Solutions Class 7 Chapter 18 Symmetry

(iii) A parallelogram is a quadrilateral with rotational symmetry of order 2 but no line of symmetry.

RD Sharma Solutions Class 7 Chapter 18 Symmetry

(iv) A quadrilateral with just one line of symmetry and no rotational symmetry is called a kite.

RD Sharma Solutions Class 7 Chapter 18 Symmetry

 

Question :8. Fill in the blanks:

RD Sharma Solutions Class 7 Chapter 18 Symmetry

Solution 8:

RD Sharma Solutions Class 7 Chapter 18 Symmetry


Question :9. Fill in the blanks:

RD Sharma Solutions Class 7 Chapter 18 Symmetry

Solution 9:

RD Sharma Solutions Class 7 Chapter 18 Symmetry
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RS Aggarwal Class 7 Mathematics Solutions Chapter 2 Fractions
RS Aggarwal Class 7 Mathematics Solutions Chapter 3 Decimals
RS Aggarwal Class 7 Mathematics Solutions Chapter 4 Rational Numbers
RS Aggarwal Class 7 Mathematics Solutions Chapter 5 Exponents
RS Aggarwal Class 7 Mathematics Solutions Chapter 6 Algebraic Expressions
RS Aggarwal Class 7 Mathematics Solutions Chapter 7 Linear Equations in One Variable
RS Aggarwal Class 7 Mathematics Solutions Chapter 8 Ratio and Proportion
RS Aggarwal Class 7 Mathematics Solutions Chapter 9 Unitary Method
RS Aggarwal Class 7 Mathematics Solutions Chapter 10 Percentage
RS Aggarwal Class 7 Mathematics Solutions Chapter 11 Profit and Loss
RS Aggarwal Class 7 Mathematics Solutions Chapter 12 Simple Interest
RS Aggarwal Class 7 Mathematics Solutions Chapter 13 Lines and Angles
RS Aggarwal Class 7 Mathematics Solutions Chapter 14 Properties of Parallel Lines
RS Aggarwal Class 7 Mathematics Solutions Chapter 15 Properties of Triangles
RS Aggarwal Class 7 Mathematics Solutions Chapter 16 Congruence
RS Aggarwal Class 7 Mathematics Solutions Chapter 17 Constructions
RS Aggarwal Class 7 Mathematics Solutions Chapter 18 Reflection and Rotational Symmetry
RS Aggarwal Class 7 Mathematics Solutions Chapter 19 Three-Dimensional Shapes
RS Aggarwal Class 7 Mathematics Solutions Chapter 20 Mensuration
RS Aggarwal Class 7 Mathematics Solutions Chapter 21 Collection and Organisation of Data
RS Aggarwal Class 7 Mathematics Solutions Chapter 22 Bar Graph
RS Aggarwal Class 7 Mathematics Solutions Chapter 23 Probability
RD Sharma Solutions Class 7 Maths
RD Sharma Solutions Class 7 Chapter 1 Integers
RD Sharma Solutions Class 7 Chapter 2 Fraction
RD Sharma Solutions Class 7 Chapter 3 Decimals
RD Sharma Solutions Class 7 Chapter 4 Rational Numbers
RD Sharma Solutions Class 7 Chapter 5 Operation on Decimal Numbers
RD Sharma Solutions Class 7 Chapter 6 Exponents
RD Sharma Solutions Class 7 Chapter 7 Algebraic Expressions
RD Sharma Solutions Class 7 Chapter 8 Linear Equations in One Variable
RD Sharma Solutions Class 7 Chapter 9 Ratio and Proportion
RD Sharma Solutions Class 7 Chapter 10 Unitary Method
RD Sharma Solutions Class 7 Chapter 11 Percentage
RD Sharma Solutions Class 7 Chapter 12 Profit and Loss
RD Sharma Solutions Class 7 Chapter 13 Simple Interest
RD Sharma Solutions Class 7 Chapter 14 Line and Angles
RD Sharma Solutions Class 7 Chapter 15 Properties of Triangle
RD Sharma Solutions Class 7 Chapter 16 Congruence
RD Sharma Solutions Class 7 Chapter 17 Constructions
RD Sharma Solutions Class 7 Chapter 18 Symmetry
RD Sharma Solutions Class 7 Chapter 19 Visualising Solid Shapes
RD Sharma Solutions Class 7 Chapter 20 Mensuration Perimeter and Area of Rectilinear Figures
RD Sharma Solutions Class 7 Chapter 21 Mensuration Area of Circle
RD Sharma Solutions Class 7 Chapter 22 Data Handling Collection and Organisation of Data
RD Sharma Solutions Class 7 Chapter 23 Data Handling Central Values
RD Sharma Solutions Class 7 Chapter 24 Data Handling Constructions of Bar Graph
RD Sharma Solutions Class 7 Chapter 25 Data Handling Probability
RS Aggarwal Class 7 Mathematics Solutions
RS Aggarwal Class 7 Mathematics Solutions Chapter 1 Integers
RS Aggarwal Class 7 Mathematics Solutions Chapter 2 Fractions
RS Aggarwal Class 7 Mathematics Solutions Chapter 3 Decimals
RS Aggarwal Class 7 Mathematics Solutions Chapter 4 Rational Numbers
RS Aggarwal Class 7 Mathematics Solutions Chapter 5 Exponents
RS Aggarwal Class 7 Mathematics Solutions Chapter 6 Algebraic Expressions
RS Aggarwal Class 7 Mathematics Solutions Chapter 7 Linear Equations in One Variable
RS Aggarwal Class 7 Mathematics Solutions Chapter 8 Ratio and Proportion
RS Aggarwal Class 7 Mathematics Solutions Chapter 9 Unitary Method
RS Aggarwal Class 7 Mathematics Solutions Chapter 10 Percentage
RS Aggarwal Class 7 Mathematics Solutions Chapter 11 Profit and Loss
RS Aggarwal Class 7 Mathematics Solutions Chapter 12 Simple Interest
RS Aggarwal Class 7 Mathematics Solutions Chapter 13 Lines and Angles
RS Aggarwal Class 7 Mathematics Solutions Chapter 14 Properties of Parallel Lines
RS Aggarwal Class 7 Mathematics Solutions Chapter 15 Properties of Triangles
RS Aggarwal Class 7 Mathematics Solutions Chapter 16 Congruence
RS Aggarwal Class 7 Mathematics Solutions Chapter 17 Constructions
RS Aggarwal Class 7 Mathematics Solutions Chapter 18 Reflection and Rotational Symmetry
RS Aggarwal Class 7 Mathematics Solutions Chapter 19 Three-Dimensional Shapes
RS Aggarwal Class 7 Mathematics Solutions Chapter 20 Mensuration
RS Aggarwal Class 7 Mathematics Solutions Chapter 21 Collection and Organisation of Data
RS Aggarwal Class 7 Mathematics Solutions Chapter 22 Bar Graph
RS Aggarwal Class 7 Mathematics Solutions Chapter 23 Probability