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Mathematics

Symmetry and Reflection Worksheet

Symmetry and Geometric Reflection
Date: May 31, 2026  •  40 questions  •  Total: 100 points
StudentAayush Nayak
Class6-B
GradeGrade 6
SchoolYBIS
1. True / False (1 pts)
The angle of symmetry of every figure is always 360°.
✓ Answer
True
2. True / False (1 pts)
A square always has more lines of symmetry than a rectangle.
✓ Answer
True
3. True / False (1 pts)
An isosceles triangle has exactly 2 lines of symmetry.
✓ Answer
False
4. True / False (1 pts)
The letter H has both vertical and horizontal lines of symmetry.
✓ Answer
True
5. True / False (1 pts)
A butterfly can exhibit symmetry even if it appears to have only one wing.
✓ Answer
True
6. True / False (1 pts)
All regular pentagons have multiple lines of symmetry.
✓ Answer
True
7. True / False (1 pts)
Circles have an infinite number of lines of symmetry.
✓ Answer
True
8. True / False (1 pts)
An isosceles triangle has exactly one line of symmetry.
✓ Answer
True
9. True / False (1 pts)
Scalene triangles have at least one line of symmetry.
✓ Answer
False
10. True / False (1 pts)
A regular hexagon can have multiple lines of symmetry.
✓ Answer
True
11. Multiple Choice (2 pts)
How many lines of symmetry are there in a rectangle?
✓ Answer
B. 2
12. Multiple Choice (2 pts)
Which of the following does not have any lines of symmetry?
✓ Answer
C. Scalene Triangle
13. Multiple Choice (2 pts)
Which of the following has two lines of symmetry?
✓ Answer
A. Rectangle
14. Multiple Choice (2 pts)
Which letter is known to have both vertical and horizontal lines of symmetry?
✓ Answer
A. X
15. Multiple Choice (2 pts)
How many lines of symmetry are there in an isosceles triangle?
✓ Answer
A. 1
16. Multiple Choice (2 pts)
Which type of symmetry is most commonly observed for the letter C?
✓ Answer
B. Horizontal
17. Multiple Choice (2 pts)
A regular pentagon has how many lines of symmetry?
✓ Answer
A. 5
18. Multiple Choice (2 pts)
An infinite number of lines of symmetry can be drawn in which shape?
✓ Answer
B. Circle
19. Multiple Choice (2 pts)
Which shape typically has an order of rotational symmetry equal to 2?
✓ Answer
B. Rectangle
20. Multiple Choice (2 pts)
What is the main characteristic of reflection symmetry?
✓ Answer
B. Each half is a mirror image
21. Fill in the Blank (2 pts)
_____ letters in the English alphabet look the same after a half turn (180 degrees).
✓ Answer
some
22. Fill in the Blank (2 pts)
All rectangles have an order of rotational symmetry of _____.
✓ Answer
2
23. Fill in the Blank (2 pts)
All squares have an order of rotational symmetry of _____.
✓ Answer
4
24. Fill in the Blank (2 pts)
The order of rotational symmetry of an equilateral triangle is _____.
✓ Answer
3
25. Fill in the Blank (2 pts)
A scalene triangle has _____ lines of symmetry.
✓ Answer
0
26. Fill in the Blank (2 pts)
An isosceles triangle has _____ line of symmetry.
✓ Answer
1
27. Fill in the Blank (2 pts)
A regular pentagon has _____ lines of symmetry.
✓ Answer
5
28. Fill in the Blank (2 pts)
A circle has an infinite number of lines of symmetry, which can be described as _____.
✓ Answer
infinite
29. Fill in the Blank (2 pts)
The butterfly's wings are _____.
✓ Answer
symmetrical
30. Fill in the Blank (2 pts)
Reflection symmetry means that one side is the _____ image of the other.
✓ Answer
mirror
31. Word Problem (5 pts)
A rectangle has 2 lines of symmetry. If a pattern repeats every 180° rotation, how many times will it repeat in a full 360° rotation? Show your working.
✎ Worked Solution
Step 1: Recognize that a 360° rotation divided by 180° equals 2.
Step 2: Therefore, the pattern repeats 2 times in a full rotation.
Answer: 2
32. Word Problem (5 pts)
A square has 4 lines of symmetry. Calculate the total number of unique reflective symmetries a square has (considering vertical, horizontal, and the two diagonal axes). Show your working.
✎ Worked Solution
Step 1: Identify the vertical, horizontal, and two diagonal lines.
Step 2: Total reflective symmetries = 4.
Answer: 4
33. Word Problem (5 pts)
If an equilateral triangle has an order of rotational symmetry of 3, by what angle is it rotated each time to map onto itself? Show your working.
✎ Worked Solution
Step 1: Divide 360° by the order 3.
Step 2: 360° / 3 = 120°.
Answer: 120°
34. Word Problem (5 pts)
A circle has an infinite number of lines of symmetry. If you draw 12 equally spaced lines through its center, do you lose the property of infinite symmetry? Show your working.
✎ Worked Solution
Step 1: Recognize that drawing any finite number of lines does not change the inherent properties of a circle.
Step 2: The circle still has infinite lines of symmetry.
Answer: No, the circle retains infinite symmetry.
35. Word Problem (5 pts)
A rectangle has 2 lines of symmetry while a square has 4. By what factor is the number of lines increased from a rectangle to a square? Show your working.
✎ Worked Solution
Step 1: Note that a square has 4 lines and a rectangle has 2 lines.
Step 2: Factor = 4 / 2 = 2.
Answer: 2
36. Word Problem (5 pts)
Given that an isosceles triangle has 1 line of symmetry and a scalene triangle has 0, how many more lines of symmetry does an isosceles triangle have compared to a scalene triangle? Show your working.
✎ Worked Solution
Step 1: Isosceles triangle lines = 1, Scalene triangle lines = 0.
Step 2: Difference = 1 - 0 = 1.
Answer: 1
37. Word Problem (5 pts)
If a regular pentagon has 5 lines of symmetry, what is the sum of its lines of symmetry and its order of rotational symmetry? Show your working.
✎ Worked Solution
Step 1: Regular pentagon has 5 lines of symmetry.
Step 2: Its rotational symmetry order is also 5.
Step 3: Sum = 5 + 5 = 10.
Answer: 10
38. Word Problem (5 pts)
Consider a butterfly with 2 lines of symmetry. If one wing is folded over, how many lines of symmetry remain visible? Show your working.
✎ Worked Solution
Step 1: Originally, the butterfly has 2 lines of symmetry.
Step 2: Folding one wing typically reveals only the vertical line of symmetry.
Answer: 1
39. Word Problem (5 pts)
If the word 'SYMMETRY' has letters with varying symmetries and the average number of symmetry lines per letter is 1, what is the total expected number of symmetry lines for the 8-letter word? Show your working.
✎ Worked Solution
Step 1: Average symmetry lines per letter = 1.
Step 2: Total letters = 8.
Step 3: Total symmetry lines = 1 x 8 = 8.
Answer: 8
40. Word Problem (5 pts)
A regular hexagon has 6 lines of symmetry. If each line divides the hexagon into two congruent parts, how many congruent regions are formed when all lines are drawn? Show your working.
✎ Worked Solution
Step 1: Drawing all 6 lines of symmetry in a regular hexagon divides it into multiple regions.
Step 2: The intersecting lines create 12 congruent regions.
Answer: 12