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Mathematics
Class 6 Mathematics — Symmetry: Lines and Rotations
Symmetry (Lines of Symmetry and Rotational Symmetry)
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
A scalene triangle has no line of symmetry.
True
False
Answer:
True
2.
1 pt
True / False
A rectangle has exactly one line of symmetry.
True
False
Answer:
False
3.
1 pt
True / False
A regular hexagon has rotational symmetry of order 6.
True
False
Answer:
True
4.
1 pt
True / False
A kite always has two lines of symmetry.
True
False
Answer:
False
5.
1 pt
True / False
A circle has rotational symmetry for every angle of rotation.
True
False
Answer:
True
6.
1 pt
True / False
A generic parallelogram (that is not a rectangle or rhombus) has no line of symmetry.
True
False
Answer:
True
7.
1 pt
True / False
Folding a figure along one of its lines of symmetry will make the two halves coincide.
True
False
Answer:
True
8.
1 pt
True / False
The smallest angle of rotation for a regular pentagon is 60°.
True
False
Answer:
False
9.
1 pt
True / False
An equilateral triangle has exactly two lines of symmetry.
True
False
Answer:
False
10.
1 pt
True / False
The uppercase letters M and W (in standard block style) have the same number of lines of symmetry.
True
False
Answer:
True
11.
2 pts
Multiple Choice
Which shape has no line of symmetry but has rotational symmetry of order 2?
A. Rectangle
B. Rhombus
C. Parallelogram (not a rectangle)
D. Isosceles trapezium
Answer:
C. Parallelogram (not a rectangle)
12.
2 pts
Multiple Choice
What is the smallest angle that maps a regular octagon to itself?
A. 36°
B. 45°
C. 60°
D. 90°
Answer:
B. 45°
13.
2 pts
Multiple Choice
How many lines of symmetry does a regular five-pointed star (pentagram) have?
A. 0
B. 2
C. 5
D. 10
Answer:
C. 5
14.
2 pts
Multiple Choice
An isosceles triangle with a horizontal base has which line of symmetry?
A. A vertical line through the apex and midpoint of the base
B. A horizontal line along the base
C. A diagonal line through one side
D. None
Answer:
A. A vertical line through the apex and midpoint of the base
15.
2 pts
Multiple Choice
What is the order of rotational symmetry of a square?
A. 1
B. 2
C. 3
D. 4
Answer:
D. 4
16.
2 pts
Multiple Choice
How many lines of symmetry does a regular dodecagon have?
A. 6
B. 8
C. 10
D. 12
Answer:
D. 12
17.
2 pts
Multiple Choice
If the smallest angle of rotation for a figure is 120°, what is the order of its rotational symmetry?
A. 2
B. 3
C. 4
D. 6
Answer:
B. 3
18.
2 pts
Multiple Choice
Which statement is true for a rhombus that is not a square?
A. It has exactly two lines of symmetry (its diagonals) and rotational order 2.
B. It has no line of symmetry and rotational order 1.
C. It has four lines of symmetry and rotational order 4.
D. It has one line of symmetry and rotational order 3.
Answer:
A. It has exactly two lines of symmetry (its diagonals) and rotational order 2.
19.
2 pts
Multiple Choice
Which transformation makes a figure coincide with itself across a symmetry line?
A. Translation
B. Reflection over that line
C. Rotation about a corner
D. Enlargement
Answer:
B. Reflection over that line
20.
2 pts
Multiple Choice
Which shape has exactly one line of symmetry and no rotational symmetry (other than a full turn)?
A. Isosceles triangle
B. Rectangle
C. Regular hexagon
D. Scalene triangle
Answer:
A. Isosceles triangle
21.
2 pts
Fill in the Blank
The smallest angle that maps a square onto itself is _____ degrees.
Answer:
90°
22.
2 pts
Fill in the Blank
A figure that looks unchanged after a half-turn has rotational symmetry of order _____.
Answer:
2
23.
2 pts
Fill in the Blank
An equilateral triangle has _____ lines of symmetry.
Answer:
3
24.
2 pts
Fill in the Blank
A regular n-gon has _____ lines of symmetry.
Answer:
n
25.
2 pts
Fill in the Blank
Reflecting a shape across its line of symmetry produces two _____ halves.
Answer:
congruent
26.
2 pts
Fill in the Blank
A circle has an _____ number of lines of symmetry.
Answer:
infinite
27.
2 pts
Fill in the Blank
The angle between adjacent spokes in a 12-spoke wheel is _____ degrees.
Answer:
30°
28.
2 pts
Fill in the Blank
A generic parallelogram (not a rectangle or rhombus) has _____ line(s) of symmetry.
Answer:
0
29.
2 pts
Fill in the Blank
The smallest angle of rotation for a regular pentagon is _____.
Answer:
72°
30.
2 pts
Fill in the Blank
Folding along a line of symmetry makes the two sides _____.
Answer:
coincide
31.
5 pts
Word Problem
A festival logo shows 8 identical petals equally spaced around a center. (a) What is the order of rotational symmetry? (b) What is the smallest angle that maps the logo onto itself? Show your working.
Working:
Answer:
Worked Solution:
Step 1: Identify number of repeated parts n = 8.
Step 2: Order of rotational symmetry = n = 8.
Step 3: Smallest angle = 360° ÷ n = 360° ÷ 8 = 45°.
Answer: Order 8; smallest angle 45°.
32.
5 pts
Word Problem
A regular polygon has each interior angle measuring 140°. Find (a) the number of sides, (b) the number of lines of symmetry, and (c) the smallest angle of rotation. Show your working.
Working:
Answer:
Worked Solution:
Step 1: Use interior angle formula: ((n − 2) × 180°) ÷ n = 140°.
Step 2: 180n − 360 = 140n ⇒ 40n = 360 ⇒ n = 9.
Step 3: Lines of symmetry for a regular n-gon = n = 9.
Step 4: Smallest angle of rotation = 360° ÷ n = 360° ÷ 9 = 40°.
Answer: (a) 9 sides, (b) 9 lines of symmetry, (c) 40°.
33.
5 pts
Word Problem
A pattern looks the same after a rotation of 24°. How many distinct orientations will it have in one full turn, and what is its order of rotational symmetry? Show your working.
Working:
Answer:
Worked Solution:
Step 1: Number of repeats in a full turn = 360° ÷ 24°.
Step 2: 360 ÷ 24 = 15.
Step 3: Order of rotational symmetry equals the number of repeats = 15.
Answer: 15 distinct orientations; order 15.
34.
5 pts
Word Problem
A wheel has 18 evenly spaced spokes. (a) What is the smallest non-zero angle that maps it onto itself? (b) How many rotational symmetries does it have (including the full turn)? Show your working.
Working:
Answer:
Worked Solution:
Step 1: Smallest angle = 360° ÷ number of spokes = 360° ÷ 18 = 20°.
Step 2: The order of rotational symmetry equals the number of spokes = 18.
Answer: (a) 20°, (b) 18 rotational symmetries.
35.
5 pts
Word Problem
A badge shows 10 identical points arranged evenly around a center (like a starburst). Determine (a) the order of rotational symmetry, (b) the smallest angle of rotation, and (c) the number of lines of symmetry if the points are placed at equal angles. Show your working.
Working:
Answer:
Worked Solution:
Step 1: Count repeated features: n = 10.
Step 2: Order of rotational symmetry = n = 10.
Step 3: Smallest angle = 360° ÷ 10 = 36°.
Step 4: For an evenly spaced, regular arrangement, lines of symmetry = n = 10.
Answer: (a) Order 10, (b) 36°, (c) 10 lines of symmetry.
36.
5 pts
Word Problem
A designer wants a logo that repeats perfectly after every 30° turn. (a) How many identical sectors will the logo have? (b) What is its rotational symmetry order? Show your working.
Working:
Answer:
Worked Solution:
Step 1: Number of sectors = 360° ÷ 30° = 12.
Step 2: Order of rotational symmetry equals number of sectors = 12.
Answer: (a) 12 sectors, (b) order 12.
37.
5 pts
Word Problem
A square sheet is folded along its vertical line of symmetry. A single hole is punched 3 cm to the right of the fold. After unfolding, how many holes appear, and where are they relative to the fold? Show your working.
Working:
Answer:
Worked Solution:
Step 1: Folding along a symmetry line creates mirror points on reopening.
Step 2: One punch through two layers produces two holes symmetric about the fold.
Step 3: Distances from the fold are equal to the original 3 cm on each side.
Answer: Two holes; one 3 cm to the right and one 3 cm to the left of the fold.
38.
5 pts
Word Problem
A regular polygon has rotational symmetry of order 9. Find (a) the angle of each step of rotation, and (b) the number of lines of symmetry. Show your working.
Working:
Answer:
Worked Solution:
Step 1: Angle per step = 360° ÷ order = 360° ÷ 9 = 40°.
Step 2: For a regular polygon, lines of symmetry = number of sides = order = 9.
Answer: (a) 40°, (b) 9 lines of symmetry.
39.
5 pts
Word Problem
A clock face is redesigned with 12 identical marks (no numbers). Determine (a) the order of rotational symmetry, and (b) the smallest rotation that maps it onto itself. Show your working.
Working:
Answer:
Worked Solution:
Step 1: With 12 identical, evenly spaced marks, n = 12.
Step 2: Order of rotational symmetry = n = 12.
Step 3: Smallest rotation = 360° ÷ 12 = 30°.
Answer: (a) Order 12, (b) 30°.
40.
5 pts
Word Problem
Each interior angle of a regular polygon is 165°. Find (a) the number of sides, (b) the number of lines of symmetry, and (c) the smallest angle of rotation. Show your working.
Working:
Answer:
Worked Solution:
Step 1: Use ((n − 2) × 180°) ÷ n = 165°.
Step 2: 180n − 360 = 165n ⇒ 15n = 360 ⇒ n = 24.
Step 3: Lines of symmetry for a regular n-gon = n = 24.
Step 4: Smallest angle of rotation = 360° ÷ 24 = 15°.
Answer: (a) 24 sides, (b) 24 lines of symmetry, (c) 15°.
40
Total Questions
100
Total Points
~35
Minutes