Generated May 31, 2026 at 1:44 PM from Ch14N.pdf
Mathematics
Symmetry and Reflection Worksheet
Symmetry and Geometric Reflection
100 pts
40 questions • ~35 min
Aayush Nayak
6-B
Grade 6
YBIS
Home
Read each question carefully and answer to the best of your ability. Show all working for word problems.
1.
1 pt
True / False
The angle of symmetry of every figure is always 360°.
True
False
Answer:
True
2.
1 pt
True / False
A square always has more lines of symmetry than a rectangle.
True
False
Answer:
True
3.
1 pt
True / False
An isosceles triangle has exactly 2 lines of symmetry.
True
False
Answer:
False
4.
1 pt
True / False
The letter H has both vertical and horizontal lines of symmetry.
True
False
Answer:
True
5.
1 pt
True / False
A butterfly can exhibit symmetry even if it appears to have only one wing.
True
False
Answer:
True
6.
1 pt
True / False
All regular pentagons have multiple lines of symmetry.
True
False
Answer:
True
7.
1 pt
True / False
Circles have an infinite number of lines of symmetry.
True
False
Answer:
True
8.
1 pt
True / False
An isosceles triangle has exactly one line of symmetry.
True
False
Answer:
True
9.
1 pt
True / False
Scalene triangles have at least one line of symmetry.
True
False
Answer:
False
10.
1 pt
True / False
A regular hexagon can have multiple lines of symmetry.
True
False
Answer:
True
11.
2 pts
Multiple Choice
How many lines of symmetry are there in a rectangle?
A. 1
B. 2
C. 0
D. 4
Answer:
B. 2
12.
2 pts
Multiple Choice
Which of the following does not have any lines of symmetry?
A. Square
B. Circle
C. Scalene Triangle
D. Equilateral Triangle
Answer:
C. Scalene Triangle
13.
2 pts
Multiple Choice
Which of the following has two lines of symmetry?
A. Rectangle
B. Square
C. Parallelogram
D. Triangle
Answer:
A. Rectangle
14.
2 pts
Multiple Choice
Which letter is known to have both vertical and horizontal lines of symmetry?
A. X
B. Z
C. T
D. F
Answer:
A. X
15.
2 pts
Multiple Choice
How many lines of symmetry are there in an isosceles triangle?
A. 1
B. 2
C. 3
D. 0
Answer:
A. 1
16.
2 pts
Multiple Choice
Which type of symmetry is most commonly observed for the letter C?
A. Vertical
B. Horizontal
C. Rotational
D. None
Answer:
B. Horizontal
17.
2 pts
Multiple Choice
A regular pentagon has how many lines of symmetry?
A. 5
B. 2
C. 1
D. 0
Answer:
A. 5
18.
2 pts
Multiple Choice
An infinite number of lines of symmetry can be drawn in which shape?
A. Square
B. Circle
C. Triangle
D. Pentagon
Answer:
B. Circle
19.
2 pts
Multiple Choice
Which shape typically has an order of rotational symmetry equal to 2?
A. Equilateral Triangle
B. Rectangle
C. Regular Pentagon
D. Circle
Answer:
B. Rectangle
20.
2 pts
Multiple Choice
What is the main characteristic of reflection symmetry?
A. Lines remain unchanged after rotation
B. Each half is a mirror image
C. Figures enlarge after reflection
D. Only applies to letters
Answer:
B. Each half is a mirror image
21.
2 pts
Fill in the Blank
_____ letters in the English alphabet look the same after a half turn (180 degrees).
Answer:
some
22.
2 pts
Fill in the Blank
All rectangles have an order of rotational symmetry of _____.
Answer:
2
23.
2 pts
Fill in the Blank
All squares have an order of rotational symmetry of _____.
Answer:
4
24.
2 pts
Fill in the Blank
The order of rotational symmetry of an equilateral triangle is _____.
Answer:
3
25.
2 pts
Fill in the Blank
A scalene triangle has _____ lines of symmetry.
Answer:
0
26.
2 pts
Fill in the Blank
An isosceles triangle has _____ line of symmetry.
Answer:
1
27.
2 pts
Fill in the Blank
A regular pentagon has _____ lines of symmetry.
Answer:
5
28.
2 pts
Fill in the Blank
A circle has an infinite number of lines of symmetry, which can be described as _____.
Answer:
infinite
29.
2 pts
Fill in the Blank
The butterfly's wings are _____.
Answer:
symmetrical
30.
2 pts
Fill in the Blank
Reflection symmetry means that one side is the _____ image of the other.
Answer:
mirror
31.
5 pts
Word Problem
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.
Working:
Answer:
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.
5 pts
Word Problem
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.
Working:
Answer:
Worked Solution:
Step 1: Identify the vertical, horizontal, and two diagonal lines.
Step 2: Total reflective symmetries = 4.
Answer: 4
33.
5 pts
Word Problem
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.
Working:
Answer:
Worked Solution:
Step 1: Divide 360° by the order 3.
Step 2: 360° / 3 = 120°.
Answer: 120°
34.
5 pts
Word Problem
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.
Working:
Answer:
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.
5 pts
Word Problem
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.
Working:
Answer:
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.
5 pts
Word Problem
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.
Working:
Answer:
Worked Solution:
Step 1: Isosceles triangle lines = 1, Scalene triangle lines = 0.
Step 2: Difference = 1 - 0 = 1.
Answer: 1
37.
5 pts
Word Problem
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.
Working:
Answer:
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.
5 pts
Word Problem
Consider a butterfly with 2 lines of symmetry. If one wing is folded over, how many lines of symmetry remain visible? Show your working.
Working:
Answer:
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.
5 pts
Word Problem
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.
Working:
Answer:
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.
5 pts
Word Problem
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.
Working:
Answer:
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
40
Total Questions
100
Total Points
~35
Minutes