NCERT Solutions for Class 7 Maths Chapter 14 Symmetry (EX 14.3) Exercise 14.3

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NCERT Solutions for Class 7 Maths Chapter 14 Symmetry (EX 14.3) Exercise 14.3

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Access NCERT Solutions for Class 7 Chapter 14 – Symmetry Exercise 14.3

Chapter 14 of the Mathematics syllabus of the Class 7 curriculum is titled Symmetry. This chapter belongs to the coordinate section of the syllabus. In this chapter, students learn more about graphs and how two graphical representations of two images can be symmetrical. This chapter requires a lot of visual aid because it is very easy to commit negligent errors while drawing a graph if students are not clear on how to determine the scale of the graph. The NCERT Solutions Class 7 Maths Chapter 14 Exercise 14.3 in Hindi and English have an amazing demonstration of sample graphs. Even the solutions where students need to draw a graph, NCERT Solutions Class 7 Maths Chapter 14 Exercise 14.3 in Hindi and English have those depicted perfectly.  Students could click on the link below to access the NCERT Solutions Class 7 Maths Chapter 14 Exercise 14.3 in Hindi and English.

Exercise 14.3

The NCERT Solutions Class 7 Maths Chapter 14 Exercise 14.3 in Hindi and English provide solutions to the 14th chapter of the NCERT Mathematics textbook for the Class 7 curriculum. All the unsolved questions in the NCERT textbook are solved in the NCERT Solutions Class 7 Maths Chapter 14 Exercise 14.3 in Hindi and English. The NCERT Solutions Class 7 Maths Chapter 14 Exercise 14.3 in Hindi and English are written in a very lucid and meticulous language to make sure that everyone can easily comprehend the language and the way the solutions are provided. The NCERT solutions have amazing, comprehensive abilities. The ease of access is  high for the NCERT Solutions Class 7 Maths Chapter 14 Exercise 14.3 in Hindi and English. The solutions follow the same chronology as the question markings in the NCERT textbook. This ensures that while students are solving a chapter and simultaneously using the NCERT Solutions Class 7 Maths Chapter 14 Exercise 14.3 in Hindi and English, they face no doubts or hindrances. The NCERT Solutions Class 7 Maths Chapter 14 Exercise 14.3 in Hindi and English follow all the NCERT rules and regulations. Every NCERT solution strictly adheres to the NCERT syllabus as well.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Exercise 14.3

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The NCERT Solutions Class 7 Maths Chapter 14 Exercise 14.3 in Hindi and English are extremely reliable and they have been extensively checked for errors.

Q.1

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

Ans

Equilateral triangle and regular hexagon have both line of symmetry and rotational symmetry.

Q.2

Draw, wherever possible, a rough sketch of(i) a triangle with both line and rotational symmetries of order more than 1.(ii) a triangle with only line symmetry and no rotational symmetry of order more than 1.(iii) a quadrilateral with a rotational symmetry of order more than 1 but not a line symmetry.(iv) a quadrilateral with line symmetry but not a rotational symmetry of order more than 1.

Ans

(i) Equilateral triangle has 3 lines of symmetry and rotational symmetry of order 3.

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(ii) Isosceles triangle has only 1 line of symmetry and no rotational symmetry of order more than 1.

MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfKttLearuGu1bxzLbIrVjxyKLwyUbqeduuDJXwAKbYu51MyVXgatCvAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wDYLwzYbItLDharyavP1wzZbItLDhis9wBH5garqqr1ngBPrgifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=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@BEE5@ (iii) A parallelogram is a quadrilateral which has no line of symmetry but a rotational symmetry of order 2.

MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfKttLearuGu1bxzLbIrVjxyKLwyUbqeduuDJXwAKbYu51MyVXgatCvAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wDYLwzYbItLDharyavP1wzZbItLDhis9wBH5garqqr1ngBPrgifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=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@C93F@ (iv) A kite is a quadrilateral which has only 1 line of symmetry and no rotational symmetry of order more than 1.

Q.3

If a figure has two or more lines of symmetry, should it have rotational symmetry of order more than 1?

Ans

Yes, if a figure has two or more lines of symmetry, then it will definitely have its rotational symmetry of order more than 1. MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfKttLearuGu1bxzLbIrVjxyKLwyUbqeduuDJXwAKbYu51MyVXgatCvAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wDYLwzYbItLDharyavP1wzZbItLDhis9wBH5garqqr1ngBPrgifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=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@DFD8@

Q.4

Shape Centre of Rotation Order of Rotation Angle of Rotation
Square
Rectangle
Rhombus
Equilateral Triangle
Regular Hexagon
Circle
Semi-circle

 

 

 

 

 

 

 

Ans

Shape Centre of Rotation Order of Rotation Angle of Rotation
Square Intersection point of diagonals 4 90°
Rectangle Intersection point of diagonals 2 180°
Rhombus Intersection point of diagonals 2 180°
Equilateral Triangle Intersection point of diagonals 3 120°
Regular Hexagon Intersection point of diagonals 6 60°
Circle Centre Infinite Any angle
Semi-circle Centre 1 360°

Q.5

Name the quadrilaterals which have both line and rotational symmetry of order more than 1.

Ans

Square, rectangle and rhombus are the quadrilaterals which have both line and rotational symmetry of order more than 1. A square has 4 lines of symmetry and rotational symmetry of order 4.A rectangle has 2 lines of symmetry and rotational symmetry of order 2.A rhombus has 2 lines of symmetry and rotational symmetry of order 2. MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfKttLearuGu1bxzLbIrVjxyKLwyUbqeduuDJXwAKbYu51MyVXgatCvAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wDYLwzYbItLDharyavP1wzZbItLDhis9wBH5garqqr1ngBPrgifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=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@DBCE@

Q.6

After rotating by 60° about a centre, a figure looks exactlythe same a sits original position.At what other angles willthis happen for the figure?

Ans

If a figure looks symmetrical on rotating by 60°, then it will also look symmetrical on rotating by 120°,180°,240°,300° and 360° i.e., further multiples of 60°. MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfKttLearuGu1bxzLbIrVjxyKLwyUbqeduuDJXwAKbYu51MyVXgatCvAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wDYLwzYbItLDharyavP1wzZbItLDhis9wBH5garqqr1ngBPrgifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=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@04F8@

Q.7

Can we have a rotational symmetry of order more than 1 whose angle of rotation is

(i) 45° ? (ii) 17° ?

Ans

If the angle of rotation of a figure is a factor of 360°, then it will have a rotational symmetry of order than 1. It can be checked that 45° will have its rotational symmetry of order more than 1. However, the figure having its angle of rotation as 17° will not be having its rotational symmetry of order more than 1. MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfKttLearuGu1bxzLbIrVjxyKLwyUbqeduuDJXwAKbYu51MyVXgatCvAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wDYLwzYbItLDharyavP1wzZbItLDhis9wBH5garqqr1ngBPrgifHhDYfgasaacH8MrFz0xbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=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@C8C4@

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