CBSE Class 6 Mathematics Symmetry Worksheet Set 05

Question 1. Find the next figure
(A)
(B)
(C)
(D) None of the options
Answer: (C)
The given sequence shows a line rotating clockwise by 90 degrees in each step with an arrow moving along the line.
In simple words: The figure rotates quarter turns clockwise.

Exam Tip: Track the position of the arrow and the main line independently.

Question 2. Find the next figure
(A)
(B)
(C)
(D)
Answer: (B)
Analyzing the rotation and intersection pattern of the intersecting lines in the sequence, the next logical rotation corresponds to option (B).
In simple words: Observe the rotational pattern of the extra intersecting lines.

Exam Tip: Count the number of intersecting hash marks in each step.

Question 3. Regular pentagon has .......line of symmetry.
Answer: 5
In simple words: A regular pentagon has 5 equal sides, so it has 5 lines of symmetry passing through each vertex and the midpoint of the opposite side.

Exam Tip: For any regular polygon with \(n\) sides, the number of lines of symmetry is equal to \(n\).

Question 4. Equilateral triangle has ........ lines of symmetry.
Answer: 3
In simple words: An equilateral triangle has 3 equal sides and 3 lines of symmetry from each vertex to the opposite side.

Exam Tip: Remember that an equilateral triangle is a regular 3-sided polygon.

Question 5. Regular hexagon has ........ lines of symmetry.
Answer: 6
In simple words: A regular hexagon has 6 equal sides and 6 lines of symmetry connecting opposite vertices and opposite sides.

Exam Tip: Regular polygons always have lines of symmetry equal to the number of their sides.

Question 6. In a complete turn (of \(360^\circ\)), the number of times an object looks exactly the same is called ........
Answer: order of rotational symmetry
In simple words: The count of identical appearances in one full rotation is the order of rotational symmetry.

Exam Tip: Order of rotational symmetry is always a whole number greater than or equal to 1.

Question 7. Rotation turns an object about a fixed point. This fixed point is the .........
Answer: center of rotation
In simple words: The fixed point around which rotation happens is called the center of rotation.

Exam Tip: The center of rotation can lie inside or outside the geometric shape.

Question 8. If, after a rotation, an object looks exactly the same, we say that it has a rotational symmetry. (True/False)
Answer: True
In simple words: An object possessing rotational symmetry matches its original form after rotating by an angle less than \(360^\circ\).

Exam Tip: Rotational symmetry requires the angle of rotation to be strictly between \(0^\circ\) and \(360^\circ\).

Question 9. If a figure has two or more lines of symmetry, should it have rotational symmetry of order more than 1?
Answer: Yes
In simple words: Multiple lines of symmetry guarantee that the figure can be rotated to coincide with itself at angles corresponding to those reflections, yielding an order of rotational symmetry greater than 1.

Exam Tip: For example, a rectangle has 2 lines of symmetry and rotational symmetry of order 2.

Question 10. A square has a rotational symmetry of order 4.
Answer: True
In simple words: A square fits onto itself 4 times during a complete \(360^\circ\) turn (at \(90^\circ, 180^\circ, 270^\circ,\) and \(360^\circ\)).

Exam Tip: Angle of rotation for a square is \(90^\circ\), and \(360^\circ / 90^\circ = 4\).

Question 11. When an object rotates, its shape and size change. (True/False)
Answer: False
In simple words: Rotation is a rigid transformation, meaning shape and size remain completely unchanged.

Exam Tip: Reflections, rotations, and translations preserve length and angle measure.

Question 12. How many symmetrical lines are possible in the given figure?
(A) 2
(B) 3
(C) 4
(D) 5
Answer: (A) 2
The stylized symmetric star/shield shape has 2 lines of symmetry (one vertical and one horizontal).
In simple words: The figure can be folded onto itself across both the vertical and horizontal axes.

Exam Tip: Check symmetry lines by testing vertical, horizontal, and diagonal folds.

Question 13. Find the next figure.
(A)
(B)
(C)
(D) None of the options
Answer: (A)
Following the sequential rotation and shifting pattern of the line segment and marker, option (A) completes the series.
In simple words: Each step rotates the component systematically.

Exam Tip: Look for consistent rotational angles between consecutive terms.

Question 14. Find the line of symmetry in the following figure. (Letter B)
(A) 0
(B) 1
(C) 2
(D) 3
Answer: (B) 1
The capital letter B has a horizontal line of symmetry running through its middle.
In simple words: The top half of letter B is the mirror reflection of its bottom half when split horizontally.

Question 15. Identify the number of lines of symmetry in a square.
(A) 1
(B) 2
(C) 3
(D) 4
Answer: (D) 4
A square has 4 lines of symmetry: 2 lines joining opposite midpoints and 2 diagonal lines.
In simple words: You can fold a square in half vertically, horizontally, and along both diagonals.

Exam Tip: A rectangle has 2 lines of symmetry, whereas a square has 4.

Question 16. Identify the number of lines of symmetry in circle.
(A) 1
(B) 2
(C) 3
(D) infinite
Answer: (D) infinite
Every line passing through the center of a circle is a line of symmetry.
In simple words: A circle is perfectly round, so it can be folded symmetrically along infinitely many diameters.

Exam Tip: A circle has an infinite number of lines of symmetry and infinite rotational symmetry order.

Question 17. Identify the number of lines of symmetry in cone.
(A) 4
(B) 3
(C) 2
(D) 1
Answer: (D) 1
A solid cone has 1 plane/line of symmetry passing down its vertical axis through the apex and the center of the circular base.
In simple words: A cone can be split into two identical halves along its central vertical axis.

Exam Tip: 3D cones have 1 plane of symmetry, which translates to 1 line of symmetry in 2D cross-sectional representation.

Question 18. Find next figure
(A)
(B)
(C)
(D)
Answer: (C)
Following the rotation rules of the given crosshairs and appended dot, option (C) correctly continues the pattern.
In simple words: The dot rotates around the center along with the intersecting axes.

Exam Tip: Trace the movement of the marker dot step-by-step.

Question 19. Find the mirror image of the given rectangle with diagonal.
(A)
(B)
(C)
(D)
Answer: (A)
Reflecting the rectangle with its diagonal across a vertical mirror reverses the diagonal's slope orientation.
In simple words: The left and right sides swap places in the mirror reflection.

Exam Tip: In horizontal reflection, points on the right move to the left and vice versa.

Question 20. Identify the number of lines of symmetry in right angle isosceles triangle.
(A) 0
(B) 1
(C) 2
(D) 3
Answer: (B) 1
A right-angled isosceles triangle has equal legs, allowing 1 line of symmetry along the angle bisector of the right angle to the hypotenuse.
In simple words: It can be folded in half along the line passing through the right angle vertex and the midpoint of the hypotenuse.

Exam Tip: Scalene triangles have 0 lines of symmetry, isosceles triangles have 1, and equilateral triangles have 3.

Question 21. Find the mirror image.
(A)
(B)
(C)
(D)
Answer: (B)
Reflecting the right-angled triangle across the vertical mirror gives triangle (B) where the vertical leg stays on the outer side and the hypotenuse mirrors its direction.
In simple words: The triangle flips horizontally.

Exam Tip: Draw perpendicular lines from each vertex to the mirror line to find exact reflected positions.

Question 22. Find the mirror image.
(A) 9
(B) 6
(C) (D)
Answer: (A) 9
The mirror image of the digit 6 across a vertical mirror is the digit 9.
In simple words: Looking at 6 in a mirror makes the loop appear on the right side, forming a 9.

Exam Tip: Mirror reflections of numbers invert left and right orientations.

Question 23. Identify the number of lines of symmetry in cylinder.
(A) 4
(B) 3
(C) 2
(D) 1
Answer: (C) 2
A cylinder has 2 planes of symmetry: one longitudinal plane passing through the axis and one perpendicular bisecting plane through its middle.
In simple words: A cylinder can be symmetrically halved lengthwise or crosswise.

Exam Tip: Consider both vertical and horizontal symmetry planes for 3D objects.

Question 24. Find the next figure.
(A)
(B)
(C)
(D)
Answer: (A)
Following the rotation sequence of the rectangle with the attached indicator node, option (A) represents the next logical position.
In simple words: The rectangle and lollipop node rotate around the center.

Exam Tip: Track the movement of the circular knob relative to the box.

Question 25. The angle of turning rotation is called the ..........
Answer: angle of rotation
In simple words: The measure of the turn during rotation is termed the angle of rotation.

Exam Tip: Common angles of rotation include \(90^\circ, 180^\circ,\) and \(360^\circ\).

Question 26. The next figure completing the sequence is
(A)
(B)
(C)
(D) None of these
Answer: (A)
The sequence rotates the marker 'A' around the circle in regular angular steps.
In simple words: Follow the clock-wise movement of letter A around the circle perimeter.

Exam Tip: Pay close attention to the position of letter labels in rotation problems.

Question 27. Name of the given figure is
(A) cube
(B) cuboid
(C) pyramid
(D) circle
Answer: (C) pyramid
The 3D shape with a triangular base and triangular faces meeting at a top apex is a triangular pyramid.
In simple words: A shape with slanted triangular faces meeting at a single top point is a pyramid.

Exam Tip: Distinguish pyramids (which taper to a single point) from prisms (which have identical parallel ends).

Question 28. Find next figure.
(A)
(B)
(C)
(D)
Answer: (A)
The lines rotate by \(90^\circ\) clockwise in each step, and option (A) shows the correct subsequent orientation.
In simple words: Each figure in the series is rotated by a quarter turn.

Exam Tip: Standard rotation angles in such puzzles are usually multiples of \(90^\circ\).

Question 29. Find the mirror image of | 0 |
(A) | | 0
(B) | 0 |
(C) 0 | |
(D) none of these
Answer: (B) | 0 |
The symbol sequence | 0 | is symmetrical, so its mirror image remains | 0 |.
In simple words: Since the left and right elements are identical, the reflection looks exactly the same.

Exam Tip: Symmetrical arrangements do not change upon reflection across a central mirror.

Question 30. Find the mirror image.
(A)
(B)
(C)
(D)
Answer: (A)
Reflecting the box with corner labels across a vertical mirror switches the position of the labels from left to right.
In simple words: The label '0' on the right reflects to the left side.

Exam Tip: Check relative corner positions to verify mirror correctness.

Question 31. Identify the number of lines of symmetry in the given figure.
(A) 1
(B) 2
(C) 3
(D) 4
Answer: (B) 2
A standard rectangular card with asymmetrical markings or a standard rectangle has 2 lines of symmetry (if plain) or corresponding to its rectangular bounds.
In simple words: A rectangle has two symmetry lines: horizontal and vertical.

Exam Tip: Rectangles always possess exactly 2 lines of symmetry.

Question 32. Identify the number of lines of symmetry in following figure (Parallelogram)
(A) 0
(B) 2
(C) 3
(D) 4
Answer: (A) 0
A general parallelogram has no lines of symmetry.
In simple words: You cannot fold a general parallelogram in half such that both halves match perfectly.

Exam Tip: Remember that a general parallelogram and a scalene triangle have 0 lines of symmetry.

Question 33. Identify the number of lines of symmetry in rectangle.
(A) 1
(B) 2
(C) 3
(D) 4
Answer: (B) 2
A rectangle has 2 lines of symmetry: one connecting the midpoints of opposite parallel sides horizontally, and one vertically.
In simple words: A rectangle can be folded horizontally and vertically into identical halves.

Exam Tip: Diagonals of a rectangle are NOT lines of symmetry because they do not overlap when folded.

Question 34. Find the axes of symmetry of the given figure?
(A) vertical
(B) horizontal
(C) diagonal
(D) none of these
Answer: (C) diagonal
A square with diagonal dots/holes possesses diagonal axes of symmetry.
In simple words: The symmetry runs along the diagonal line connecting opposite corners.

Exam Tip: Look at the alignment of internal features to determine symmetry axes.

Question 35. Find the mirror image
(A)
(B)
(C)
(D) None of these
Answer: (B)
The mirror image of the capital letter N across a vertical mirror flips its diagonal stroke.
In simple words: The diagonal leg of N reverses direction in the mirror.

Exam Tip: Capital N reflected vertically looks like a reversed N.

Question 36. Find the mirror image.
(A)
(B)
(C)
(D)
Answer: (B)
Reflecting the circle with a diametric line segment across a vertical mirror inverts the slope of the diameter.
In simple words: The slant inside the circle flips orientation.

Exam Tip: Check the angle of the line inside the circle relative to the mirror axis.

Question 37. Find the mirror image. (Letter L)
(A)
(B)
(C)
(D)
Answer: (A)
The mirror image of the capital letter L across a vertical line points to the left instead of the right.
In simple words: The horizontal base of L points leftwards in the mirror reflection.

Exam Tip: Asymmetric letters change their orientation completely upon mirror reflection.

Question 38. How many symmetrical lines are possible in the given figure? (Hourglass/I-shape)
(A) 1
(B) 2
(C) 3
(D) 4
Answer: (B) 2
The dumbbell/hourglass shaped figure has 2 lines of symmetry (one horizontal and one vertical).
In simple words: It can be folded symmetrically along both its vertical centerline and horizontal centerline.

Exam Tip: Symmetric shapes with crossbars typically have two perpendicular symmetry lines.

Question 39. Identify the numbers of lines of symmetry in following figure. (Letter M)
(A) 0
(B) 2
(C) 3
(D) 1
Answer: (D) 1
The capital letter M has 1 vertical line of symmetry down its exact middle.
In simple words: The right half of M is an exact mirror image of its left half.

Exam Tip: Letters like A, M, T, V, W, Y have a single vertical line of symmetry.

Question 40. Copy the following figure with punched holes and find the axes of symmetry for the following:
Answer:
1. Copy the given rectangular card with four punched holes near each corner onto a sheet of paper.
2. Draw dashed lines joining the midpoints of opposite sides (horizontal and vertical lines of symmetry).
3. Draw both diagonal lines connecting opposite corners.
4. The axes of symmetry for this rectangular configuration with symmetric holes are the horizontal line and the vertical line passing through the center.
In simple words: A rectangle with symmetrically placed holes has 2 principal axes of symmetry (horizontal and vertical).

Exam Tip: Always verify that folding along the axis places the punched holes directly on top of each other.

Question 41. For the following figure identify multiple lines of symmetry.
Answer:
1. Observe the square figure containing symmetrical curved patterns or intersecting shaded arcs.
2. Identify the vertical line passing through the center.
3. Identify the horizontal line passing through the center.
4. Identify the two diagonal lines connecting the opposite corners of the square.
Conclusion: The figure has 4 lines of symmetry.
In simple words: The figure is symmetric along both vertical, horizontal, and both diagonal axes.

Exam Tip: Symmetrical designs inscribed inside a square usually share the square's 4 lines of symmetry.

Question 42. Given the lines of symmetry, find the other holes.
Answer:
1. Identify the given circle and its two intersecting lines of symmetry (diameters).
2. Given one hole in one quadrant, use reflection across the first line of symmetry to plot the corresponding hole in the adjacent quadrant.
3. Reflect the holes across the second line of symmetry to complete all four symmetrical positions.
In simple words: Reflect the existing punched hole across each symmetry line to locate the remaining symmetric holes.

Exam Tip: Every hole in a symmetric figure must have a corresponding mirror-image partner across every line of symmetry.

Question 43. Name the quadrilaterals which have both line and rotational symmetry of order more than 1.
Answer:
The quadrilaterals that possess both line symmetry and rotational symmetry of order greater than 1 are:
1. Square (Line symmetry = 4, Rotational symmetry order = 4)
2. Rectangle (Line symmetry = 2, Rotational symmetry order = 2)
3. Rhombus (Line symmetry = 2, Rotational symmetry order = 2)
In simple words: Squares, rectangles, and rhombuses can be folded along lines of symmetry and rotated to match themselves.

Exam Tip: Parallelograms have rotational symmetry of order 2 but NO line symmetry, so they are excluded.

Question 44. In the following figure, the mirror line is given as a dotted line. Complete each figure performing reflection in the dotted line. Are you able to recall the name of the figure you complete?
Answer:
1. Measure perpendicular distances from each vertex of the half-figure to the dotted mirror line.
2. Plot corresponding equidistant points on the opposite side of the mirror line.
3. Join the plotted points to complete the symmetric polygon.
4. Name of the completed figure: A pentagon (or regular polygon depending on side lengths).
In simple words: Reflect every point across the dotted line to draw the missing half, forming a closed 5-sided polygon (pentagon).

Exam Tip: Use a ruler to ensure reflection points are exactly perpendicular and equal in distance from the mirror line.

Question 45. What letters of the English alphabet have reflectional symmetry about (a) a vertical mirror (b) a horizontal mirror (c) both horizontal and vertical mirrors.
Answer:
(a) Vertical mirror: A, H, I, M, O, T, U, V, W, X, Y
(b) Horizontal mirror: B, C, D, E, H, I, K, O, X
(c) Both horizontal and vertical mirrors: H, I, O, X
In simple words: Letters like H, I, O, and X look identical whether reflected vertically or horizontally.

Exam Tip: Memorize the set {H, I, O, X} as the universal letters with both horizontal and vertical symmetry.

Question 46. State the number of lines of symmetry for the following figures: (a) An equilateral triangle (b) A rectangle
Answer:
(a) An equilateral triangle has 3 lines of symmetry.
(b) A rectangle has 2 lines of symmetry.
In simple words: Equilateral triangles have 3 symmetry lines, and rectangles have 2.

Exam Tip: Regular shapes have lines of symmetry equal to their number of sides.

Question 47. What other name can you give to the line of symmetry of (a) an isosceles triangle (b) a circle
Answer:
(a) For an isosceles triangle, the line of symmetry is also the angle bisector of the vertex angle and the median/altitude to the base.
(b) For a circle, any line of symmetry is a diameter of the circle.
In simple words: In an isosceles triangle it is the altitude/median, and in a circle it is any diameter.

Exam Tip: Connecting geometric terms enhances conceptual clarity in geometry answers.

Question 48. Give the order of rotational symmetry for each figure: (a) (b) (c)
Answer:
(a) The cross/plus sign figure has rotational symmetry of order 4.
(b) The intersecting line pair with an angle of \(80^\circ\) / intersecting lines has rotational symmetry of order 2.
(c) The asymmetric arrow/flag figure has rotational symmetry of order 1.
In simple words: Figure (a) matches 4 times in a full turn, figure (b) matches 2 times, and figure (c) only matches once.

Exam Tip: Every object has at least rotational symmetry of order 1.

Question 49. Give three examples of shapes with no line of symmetry.
Answer:
1. Scalene triangle
2. General quadrilateral (that is not a parallelogram, kite, or trapezium)
3. Scalene trapezoid
In simple words: Shapes with all unequal sides and angles possess no line of symmetry.

Exam Tip: Scalene figures are the best examples for zero lines of symmetry.

Question 50. For the given alphabets given in the table complete the following table:
Answer:

In simple words: Each letter is analyzed for its reflection lines and rotational turns.

Exam Tip: Letters like Z, S, and N have rotational symmetry of order 2 but zero line symmetry.