WBBSE Solutions For Class 7 Maths Geometry Chapter 9 Symmetry Exercise 9 Solved Problems

WB Class 7 Math Solution Geometry Chapter 9 Symmetry Exercise 9 Solved Problems

Symmetry:

Symmetry means an exact similarity in shape and size between parts of an object.

Classification of Symmetry:

There are three types of symmetry-
1. Linear symmetry
2. Point symmetry and
3. Rotational symmetry.

Linear symmetry:

⇒ An Image is said to be a line of symmetry or linear symmetry if there exists a straight line which divides the figure into two identical halves that completely coincide with each other when folded about that line.

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⇒ The straight line is called the line of symmetry or line of reflection.

 

 

 

 

⇒ In the above images, the line PQ is called the line of symmetry or axis of symmetry.

Regular Polygon:

⇒ The polygon having all sides and all angles equal are called a regular polygon.

Wbbse Class 7 Maths Solutions

Axially Symmetric Images

 

 

Rotational symmetry:

⇒ If an image coincides with its image when it is rotated about a point through an angle less than 360°, the image is said to be rotational symmetry.

1. The point across which the figure rotates is called the centre of rotation.
2. The angle of rotational symmetry is the minimum angle through which a geometrical image is rotated about a point to get the first symmetrical image.
3. The number of times an object coincides with its image in the process of a complete rotation of 360° about a point is called the order of the rotational symmetry.
4. If the smallest angle of rotational symmetry of an image is x° then the order of rotational 360° symmetry is \(\frac{360°}{x°}\)
5. If 45° is the smallest angle of rotational symmetry. So the order of rotational symmetry = \(\frac{360°}{45°}\) = 8

Wbbse Class 7 Maths Solutions

Rotationally Symmetric Images

 

 

Question 1. Choose the correct answer 

1. The number of lines of symmetry of an equilateral triangle is

1. 1
2. 2
3. 3
4. 4

 

Solution: The number of line of symmetry of an equilateral triangle is 3.

⇒ So the correct answer is 3. 3

2. The number of line of symmetry of an isosceles trapezium is

1. 1
2. 2
3. 3
4. 4

 

Solution: The correct answer is 1. 1

3. If the period of rotational symmetry of an equilateral triangle be three then its angle of rotational symmetry is

1. 90°
2. 120°
3. 100°
4. 60°

Solution: The angle of rotational symmetry is \(\frac{360°}{3}\) or 120°

⇒ So the correct answer is 2. 120°

Wbbse Class 7 Maths Solutions

4. The number of axis of symmetry of a kite is

1. 0
2. 1
3. 2
4. 3

 

Solution: The number of line of symmetry of a kite is 1

⇒ So the correct answer is 2.1

5. If the angle of rotational symmetry of a regular polygon is 60°, then the number of sides is

1. 2
2. 4
3. 6
4. 7

 

Solution: The required number of sides = \(\frac{360°}{60°}\) = 6

So the correct answer is 3. 6

Question 2. Write true or false 

1. A scalene triangle has no line symmetry.

 

Solution: The statement is true.

2. The butterfly is not a symmetrical object.

 

Solution: The butterfly has one line of symmetry.

So the statement is false.

3. The order of rotational symmetry of an equilateral triangle is 2.

Solution: The angle of rotational symmetry of an equilateral triangle is 120°

⇒ So the order of rotational symmetry = \(\frac{360°}{120°}\)

⇒ So the statement is false.

4. The number of line of symmetry of a circle is infinite

 

 

Solution: As the axis of symmetry of a circle is its diameter. So there are infinite numbers of symmetry.

⇒ So the statement is true.

5. Isosceles trapezium has line and rotational symmetry.

 

Solution: Isosceles trapezium has only line of symmetry.

⇒ So the statement is false.

Question 3. Fill in the blanks 

1. If the angle of rotational symmetry of any figure is 180°, then its number of rotational symmetry will be _______

Solution: The required number of rotational symmetries is \(\frac{360°}{180°}\)

2. The angle of rotational symmetry of a square is ____ degree.

Solution: The angle of rotational symmetry of a square is\(\frac{360°}{4°}\) = 90°

3. The circle is linear and symmetric about its _____

Solution: diameter.

4. The centre of rotational symmetry of a rectangle is the point of intersection of the ______

Solution:

5. ______ has no line of symmetry but has two degrees of rotational symmetry.

 

 

Solution: parallelogram.

The center of rotational symmetry of a rectangle is the point of intersection of the diagonals.

Wbbse Class 7 Maths Solutions

Question 4. Which of the following images have line of symmetry

 

Solution:

Semicircle has one line of symmetry

 

Hexagonal has a sox line of symmetry

 

Scalene triangle has no line of summetry

Question 5. 1. Find the order of rotational symmetry.

1. Rhombus
2. Regular pentagon.

Solution:

1. The order of rotational symmetry of rhombus is \(\frac{360°}{180°}\)

2. The angle of rotation of regular pentagon is 72°

⇒ So degree of rotation = \(\frac{360°}{72°}\)= 5

2. Find the angle of rotation of a parallelogram.

Solution: The angle of rotation of a parallelogram is 180°

3.  Find the number of lines of symmetry of the butterfly. 

Solution:

⇒ The number of lines of symmetry of the butterfly is one.

WB Class 7 Math Solution Symmetry

Symmetry Exercise 9.1

Question 1. Let’s place a mirror along the line of symmetry and complete the following figure.
Solution:

Question 2. Let’s draw the reflections of A, B, C, and D in a mirror.
Solution:

Question 3. In the plane figures given below, which figures have line symmetry and which figures do not have line symmetry, let’s write and verify by cutting off the figures and folding them.
Solution:

 

Question4. Let us find a line of symmetry for
Solution:

1.  It is observed that the line of symmetry of A is Vertical
2. The line of symmetry of E is Horizontal

Question5. In the letter given below, identify which of them will have vertical which of them have horizontal, and which will have both, lines of symmetry
Solution:

E →  Horizontal lines of symmetry

H, O, X → Both horizontal & vertical of symmetry

M → Vertical line of symmetry

Question 6. Let us draw plane figures, then cut them off to find if they have rotational symmetry. Let’s write in the blank spaces given below and try to verify them.
Solution:

WBBSE Class 7 Math Solution Symmetry Exercise 9.2

Question 1. The isosceles triangle has only line symmetry.

The isosceles triangle has only line symmetry

• An equilateral triangle has line as well as rotational symmetry.
• The number of rotational symmetry of a square is 4.
• For a rectangle, the number of rotational symmetry is 2.
• There are 4 lines of symmetry for a square tut 2 lines of symmetry for a rectangle.
• Parallelogram has only rotational symmetry.
• If the angle of rotational symmetry of any figure is 1803> ‘ts number of rotational symmetry will be 2.
• A regular pentagon has line and rotational symmetry.
• For a regular hexagon, the angle of rotational symmetry is 60 degrees and its number is 6.
• Only Isosceles trapezium has line symmetry but no rotational symmetry.
• The centre of rotational symmetry of a parallelogram is 180°.
• The angle of rotational symmetry of an equilateral triangle is 120°
• The angle of rotational symmetry of a square is 90s.
• Parallelogram has no line symmetry but has two degrees of rotational symmetry.

Question 2. Which of the following geometric figures have line symmetry but don’t have rotational symmetry?

1.

1. Equilateral triangle,
2. Parallelogram,
3. Isosceles triangle,
4. Circle

Solution: Isosceles triangle

2. Which of the following geometric figures have a measure of rotational symmetry 2 but that figure has no line symmetry?

1. Rectangle
2. Parallelogram
3. Isosceles triangle
4. Circle

Solution: Parallelogram.

3. If the angle of rotational symmetry of a regular polygon be 60°, then its number of sides

1. 4
2. 4
3. 6
4. 7

Solution:  6.

4.  Which of the following figures have two lines of symmetry and the angles of rotational symmetry 180°
Solution:  Rectangle.

Question 3. Let’s observe the pictures and complete the chart given below
Solution: