Class 7 Maths Chapter 12 Practice Question Answers - Symmetry

Q1. Which of the following figures has no line of symmetry?
(a) Square
(b) Circle
(c) Triangle
(d) Rectangle
Ans: (b)
Sol: A circle has infinite lines of symmetry, but none of them is a "line" of symmetry because a circle is symmetrical about any line passing through its center.

Q2. Which of the following alphabet has vertical line of symmetry?
(a) A
(b) B
(c) Q
(d) E
Ans: (a)
Sol:
Option A is correct because Left side of line is the mirror image of right one and vise versa.

Q3. Which of the following figure(s) have only one line of symmetry?
(a)
(b)
(c)
(d)
Ans: (b)
Sol:
Resulting figure of option B
Only Option B has one line of symmetry that is vertical line of symmetry rest all have more than one line of symmetry

Q4. Which of the following alphabet has horizontal line of symmetry ?
(a) B
(b) E
(c) H
(d) All of the above
Ans: (d)
Sol:
As shown in figure we have horizontal line of symmetry or figure is symmetrical above the horizontal line passing through the the B,H,E

Q5. Which of the following figures have rotational symmetry of order more than 1?
(a)
(b)
(c)
(d) All the above
Ans: (d)
Sol: Rotational symmetry of order more than 1 define that the object produces exact same image when rotated more than one about its axis. Hence all the figure shown here have more than 1 order of symmetry.

Q6. The number of lines of symmetry of the given figure is 

(a) 6
(b) 12
(c) Infinite
(d) Finite
Ans: (a)
Sol: The lines through the center of the circle and passing through (E,(b),(F,(c), or(A,(d) are three lines of symmetry. The lines through the midpoints of arcs EF and CB,FA and DC and AB through the center are the other three lines of symmetry. In total 6.

Q7. The number of lines of symmetry for a line segment are _____.
(a) Is infinite
(b) One
(c) Two
(d) None
Ans: (b)
Sol: If AB is a line segment, then a line l, which is perpendicular bisector of AB, is the line of symmetry.

Q8. The number of line symmetries that the given figure have _____
(a) 1
(b) 3
(c) 2
(d) 0
Ans: (d)
Sol: The above-mentioned figure has no lines of symmetry as it is not an equilateral triangle or symmetrical triangle. It has 0 lines of symmetry. As it is scalene triangle
Hence option D is the correct answer.

Q9. How many lines of symmetry does the parallelogram have?

(a) 2
(b) 3
(c) 4
(d) None of these
Ans: (d)
Sol: The number of lines of symmetry of a parallelogram depends on the type of parallelogram. A non-special parallelogram does not have any lines of symmetry. This includes any quadrilateral with two pairs of parallel and equal sides, except for rectangles, squares and rhombuses.
A rectangle is a parallelogram with four right angles. This property allows it to have two lines of symmetry.
A rhombus is a parallelogram with four equal sides. The number of lines of symmetry of a rhombus depends on whether it is a square or not. If it has four right angles, the rhombus is a square and thus has four lines of symmetry. If not, the rhombus only has two lines of symmetry.
So the correct answer is option (d)

Q10. The number of capital letters of the English alphabets having both horizontal and vertical lines of symmetry are ______.
(a) 0
(b) 1
(c) 4
(d) 6
Ans: (c)
Sol: We know that in A there is only vertical symmetry and in B there is only horizontal symmetry. Only H, I, O, X have both vertical and horizontal symmetries. The number of capital letters of the English alphabets having both horizontal and vertical lines of symmetry is 4 (H, I, O, X).
So,  option C is the correct answer.

Q11. The number of lines of symmetry in a picture of Taj Mahal is ______.
(a) 1
(b) 2
(c) 0
(d) 3
Ans: (a)
Sol: If you drew a line down the middle of the picture, you would notice that each side of the Taj Mahal looks exactly the same. This means the building has one line of symmetry. Symmetry is when an object looks the exact same on one side as the other.

So option A is the correct answer.

Q12. The digit having only one line of symmetry  is ______ .
(a) 0
(b) 3
(c) 5
(d) 9
Ans: (b)
Sol: Symmetry is the property of shapes which when flipped looks identical to it's original shape. A line of symmetry is a line that divides the given shape into identical parts. 0 has two lines of symmetry. It is symmetrical over both horizontal and vertical axis.
3 has one line of symmetry. Remaining numbers do not have any lines of symmetry.
So option B is the correct answer.

Q13. The number of lines of symmetry in compasses is
(a) 0
(b) 1
(c) 2
(d) 3
Ans: (a)
Sol: The number of lines of symmetry in compasses is 0.

Q14. How many  lines of symmetry of the  does the rectangle have
(a) 0
(b) 2
(c) 4
(d) 6
Ans: (b)
Sol: 
⇒  There are 2 symmetry lines of a rectangle which are from its length and breadth.
⇒  These two lines cut the rectangle in two similar halves which are mirror images of each other. If a rectangle is folded along its line of symmetry, it superimposes perfectly.
∴   Rectangle has 2 lines of symmetry.

Q15. The angle of rotation symmetry for a shape is 60° . What is the order of rotational symmetry?
(a) 6
(b) 4
(c) 3
(d) 8
Ans: (a)
Sol: A hexagon has  angle of rotation  60^∘ .Hexagon has order of rotational symmetry is 6.

Q16. Find the order of rotational symmetry of equilateral triangle.
(a) 2
(b) 3
(c) 4
(d) 5
Ans: (b)
Sol: If a equilateral triangle is rotated by 120 (one fifth of 360), then it exactly fits its own outline.

Therefore a equilateral triangle has rotational symmetry of order 3.

Q17. How many lines of symmetry are in this isosceles triangle?

(a) 1
(b) 2
(c) 3
(d) 4
Ans: (a)
Sol: An isosceles triangle has one line of symmetry. However, if the isosceles triangle is also an equilateral triangle, then it has three lines of symmetry.
But the given triangle is not an equilateral triangle.
An isosceles triangle is defined as a triangle with two sides of equal length. An equilateral triangle is defined as a triangle with three sides of equal length. Therefore, an equilateral triangle is also an isosceles triangle.
This triangle has 2 sides of equal length. When an isosceles triangle has exactly two sides of equal length, then it has just 1 line of symmetry that runs from the vertex between the two sides of equal length to the midpoint of the side opposite that vertex.
So option A is the correct answer.

Q18. Find the order of rotational symmetry of rhombus.
(a) 4
(b) 3
(c) 2
(d) 1
Ans: (c)
Sol: If a rhombus is rotated by 180^o (half of 360^o ), then it exactly fits its own outline.\
Therefore a rhombus has rotational symmetry of order 2.

Q19. If this hexagon is rotated 90^o clockwise about point A, how many lines of symmetry will there be in the diagram formed by the hexagon and its image? 

(a) 4
(b) 1
(c) 2
(d) 0
Ans: (a)
Sol:  If you can effect a figure over a line and the figure appears unchanged ,then the figure has reflection  symmetry or line symmetry . the line that you reflect over is called line of symmetry . Aline of symmetry divides figure into two mirror image .
If this hexagon is rotated 90 clockwise about point A .
Then 4 line of symmetry will be there

Q20. What is the order of rotational symmetry of a regular pentagon?
(a) 2
(b) 5
(c) 10
(d) 15
Ans: (b)
Sol: 

A pentagon has 5 rotational symmetry as shown in figure has 5 point when rotated produces symmetrical image

Q21. The line of symmetry for a line segment is along its
(a) perpendicular
(b) perpendicular bisector
(c) vertex
(d) none of the above
Ans: (b)
Sol: Line of symmetry may also be defined as the line segment along which, when the image is folded one side over the other, the upper folded area fully covers the lower folded area.
Hence line of symmetry is always along the perpendicular bisector

Q22. Which of the following letters has rotational symmetry of order 1 (no rotational symmetry)?
(a) V
(b) W
(c) U
(d) X
Ans: (a)
Sol: The letters "V" and "X" have rotational symmetry of order 1, meaning they look the same only after a full rotation of 360°.

Q23. How many lines of symmetry does a scalene triangle have?
(a) 0
(b) 1
(c) 2
(d) 3
Ans: (a)
Sol: A scalene triangle has no lines of symmetry, as its sides and angles are not equal.

Q24. Which of the following figures has rotational symmetry of order 3?
(a) Square
(b) Pentagon
(c) Equilateral triangle
(d) Rectangle
Ans: (c)
Sol: A figure with rotational symmetry of order 3 looks the same after a rotation of 120°, 240°, or 360°. An equilateral triangle has rotational symmetry of order 3.

Q25. How many lines of symmetry does a regular decagon have?
(a) 0
(b) 1
(c) 2
(d) 10
Ans: (d)
Sol: A regular decagon has ten lines of symmetry, passing through each vertex and the midpoint of the opposite side.

Q26. Which of the following letters has rotational symmetry of order 4?
(a) M
(b) N
(c) H
(d) U
Ans: (d)
Sol: The letter "U" has rotational symmetry of order 4, meaning it looks the same after a rotation of 90°, 180°, 270°, or 360°.

Q27. How many lines of symmetry does a regular nonagon have?
(a) 0
(b) 1
(c) 2
(d) 9
Ans: (d)
Sol: A regular nonagon has nine lines of symmetry, passing through each vertex and the midpoint of the opposite side.

Q28. Which of the following figures has rotational symmetry of order 5?
(a) Square
(b) Pentagon
(c) Equilateral triangle
(d) Rectangle
Ans: (b)
Sol: A figure with rotational symmetry of order 5 looks the same after a rotation of 72°, 144°, 216°, 288°, or 360°. A pentagon has rotational symmetry of order 5.

Q29. How many lines of symmetry does a regular undecagon have?
(a) 0
(b) 1
(c) 2
(d) 11
Ans: (d)
Sol: A regular undecagon has eleven lines of symmetry, passing through each vertex and the midpoint of the opposite side.

Q30. Which of the following letters has both horizontal and vertical lines of symmetry?
(a) V
(b) I
(c) H
(d) U
Ans: (b)
Sol: The letter "I" has both horizontal and vertical lines of symmetry, dividing it into four identical quarters.