Hard Level Worksheet
Very Short Answer Questions (1 Mark Each)
(1) Write the number of lines of symmetry in a regular hexagon.
A regular hexagon has
Correct! Each line passes through opposite vertices or midpoints of opposite sides.
(2) State the order of rotational symmetry of a square.
The order of rotational symmetry of a square is
Perfect! A square looks identical after rotations of
(3) Which English letter has both line symmetry and rotational symmetry?
Excellent! The letter 'H' has multiple lines of symmetry and rotational symmetry.
(4) Write the number of lines of symmetry in a rhombus.
A rhombus has
Great! The lines pass through opposite vertices (diagonals).
(5) A rectangle has 2 lines of symmetry. True or False?
Correct! One horizontal and one vertical line through the center.
Short Answer Questions (2 Marks Each)
Answer each question with clear diagrams and explanations and submit sheet to subject teacher.
(1) Draw a regular octagon. Mark its lines of symmetry.
A regular octagon has
Perfect! Draw the octagon and mark all 8 lines clearly.
(2) Explain why the letter "Z" has no line of symmetry but has rotational symmetry of order 2.
Line symmetry: It's
Rotational symmetry: Rotating Z by
Excellent analysis! Z has rotational but not reflectional symmetry.
(3) A regular pentagon has 5 lines of symmetry. Show them with a neat sketch.
(4) Draw an isosceles triangle. Show its line of symmetry. Write whether it has rotational symmetry or not.
Lines of symmetry:
Rotational symmetry:
Perfect! Only the perpendicular bisector of the base is a line of symmetry.
(5) A circle has infinite lines of symmetry. Explain why.
Every
Since there are
Excellent! Any line through the center divides the circle into identical halves.
Long Answer Questions (4 Marks Each)
Note: Answer each question with detailed diagrams and complete explanations.
(1) Draw a square and mark all its lines of symmetry. Explain why it has rotational symmetry of order 4.
Lines of symmetry: A square has
Two
Rotational symmetry order 4: Square looks identical after rotations of
(2) Draw a regular hexagon. Show all its lines of symmetry and state its rotational symmetry order.
Lines of symmetry:
Rotational symmetry order:
Perfect! Regular polygons have n lines of symmetry and order n rotational symmetry.
(3) Write the difference between line symmetry and rotational symmetry with at least two examples each.
Line Symmetry: Shape can be
Examples:
Rotational Symmetry: Shape looks
Examples:
(4) Draw a rhombus. Show its lines of symmetry. Explain why it has rotational symmetry of order 2 but not 4.
Lines of symmetry:
Rotational symmetry order
Not order 4 because: Opposite sides are
Only 180° rotation preserves the shape, not 90° or 270°.
(5) The English letter "X" has both line and rotational symmetry. Draw the figure and justify your answer.
Line symmetry:
Rotational symmetry: Order
Justification: X is symmetrical both ways due to its crossing structure with
Part B: Objective Questions (1 Mark Each)
Choose the correct answer and write the option (a/b/c/d)
(1) The number of lines of symmetry in a regular octagon is:
(a) 4 (b) 6 (c) 8 (d) 10
Correct! A regular octagon has 8 lines of symmetry.
(2) The order of rotational symmetry of an equilateral triangle is:
(a) 1 (b) 2 (c) 3 (d) 6
Correct! Equilateral triangle has rotational symmetry of order 3.
(3) Which of the following letters has 2 lines of symmetry?
(a) H (b) K (c) L (d) Z
Correct! Letter H has 2 lines of symmetry (horizontal and vertical).
(4) The number of lines of symmetry in a rectangle is:
(a) 1 (b) 2 (c) 3 (d) 4
Correct! Rectangle has 2 lines of symmetry through opposite sides' midpoints.
(5) The circle has:
(a) No line of symmetry (b) 1 line of symmetry (c) 2 lines of symmetry (d) Infinite lines of symmetry
Correct! Every diameter is a line of symmetry for a circle.
(6) Which of the following shapes has rotational symmetry but no line symmetry?
(a) Z (b) O (c) H (d) X
Correct! Z has rotational symmetry (order 2) but no line of symmetry.
(7) The order of rotational symmetry of a rectangle is:
(a) 1 (b) 2 (c) 3 (d) 4
Correct! Rectangle looks identical after 180° and 360° rotations.
(8) A rhombus has how many lines of symmetry?
(a) 1 (b) 2 (c) 3 (d) 4
Correct! Rhombus has 2 lines of symmetry along its diagonals.
(9) Which English letter has only rotational symmetry of order 2 but no line symmetry?
(a) H (b) Z (c) O (d) M
Correct! Z has rotational symmetry order 2 but no line symmetry.
(10) The number of lines of symmetry in a regular pentagon is:
(a) 3 (b) 4 (c) 5 (d) 6
Correct! Regular pentagon has 5 lines of symmetry.
Symmetry Challenge
Determine whether these statements are True or False:
Symmetry Quiz
🎉 Congratulations! What You've Mastered:
You have successfully completed the "Symmetry" hard worksheet and learned:
(1) Line Symmetry Understanding: Recognizing how shapes can be folded along lines to match exactly
(2) Rotational Symmetry Mastery: Understanding how shapes look identical after specific rotations
(3) Regular Polygon Properties: Knowing that n-sided regular polygons have n lines of symmetry and order n rotational symmetry
(4) Geometric Shape Analysis: Analyzing squares, rectangles, rhombuses, triangles, and circles for symmetry properties
(5) Letter Symmetry Recognition: Identifying which English letters have line symmetry, rotational symmetry, or both
(6) Order of Rotational Symmetry: Calculating how many times a shape looks identical during a 360° rotation
(7) Multiple Lines of Symmetry: Finding all possible lines of symmetry in complex shapes like hexagons and octagons
(8) Symmetry vs. Non-Symmetry: Distinguishing between shapes that have symmetry and those that don't
(9) Diagonal and Midpoint Lines: Understanding different types of symmetry lines in polygons
(10) Circle Symmetry Properties: Recognizing that circles have infinite lines of symmetry through any diameter
(11) Triangle Classifications: Comparing symmetry properties of equilateral, isosceles, and scalene triangles
(12) Quadrilateral Symmetry: Analyzing squares, rectangles, rhombuses, and parallelograms for their unique symmetry properties
(13) Visual Pattern Recognition: Developing the ability to see symmetrical patterns in everyday objects
(14) Mathematical Reasoning: Understanding why certain shapes have specific symmetry properties
(15) Real-world Applications: Connecting symmetry concepts to architecture, nature, and design patterns
Outstanding work! You now have a deep understanding of symmetry concepts and can identify symmetrical properties in various shapes and patterns!