StudentAayush Nayak
Class6-B
GradeGrade 6
SchoolYBIS
1.
True / False
(1 pts)
A scalene triangle has no line of symmetry.
2.
True / False
(1 pts)
A rectangle has exactly one line of symmetry.
3.
True / False
(1 pts)
A regular hexagon has rotational symmetry of order 6.
4.
True / False
(1 pts)
A kite always has two lines of symmetry.
5.
True / False
(1 pts)
A circle has rotational symmetry for every angle of rotation.
6.
True / False
(1 pts)
A generic parallelogram (that is not a rectangle or rhombus) has no line of symmetry.
7.
True / False
(1 pts)
Folding a figure along one of its lines of symmetry will make the two halves coincide.
8.
True / False
(1 pts)
The smallest angle of rotation for a regular pentagon is 60°.
9.
True / False
(1 pts)
An equilateral triangle has exactly two lines of symmetry.
10.
True / False
(1 pts)
The uppercase letters M and W (in standard block style) have the same number of lines of symmetry.
11.
Multiple Choice
(2 pts)
Which shape has no line of symmetry but has rotational symmetry of order 2?
✓ Answer
C. Parallelogram (not a rectangle)
12.
Multiple Choice
(2 pts)
What is the smallest angle that maps a regular octagon to itself?
13.
Multiple Choice
(2 pts)
How many lines of symmetry does a regular five-pointed star (pentagram) have?
14.
Multiple Choice
(2 pts)
An isosceles triangle with a horizontal base has which line of symmetry?
✓ Answer
A. A vertical line through the apex and midpoint of the base
15.
Multiple Choice
(2 pts)
What is the order of rotational symmetry of a square?
16.
Multiple Choice
(2 pts)
How many lines of symmetry does a regular dodecagon have?
17.
Multiple Choice
(2 pts)
If the smallest angle of rotation for a figure is 120°, what is the order of its rotational symmetry?
18.
Multiple Choice
(2 pts)
Which statement is true for a rhombus that is not a square?
✓ Answer
A. It has exactly two lines of symmetry (its diagonals) and rotational order 2.
19.
Multiple Choice
(2 pts)
Which transformation makes a figure coincide with itself across a symmetry line?
✓ Answer
B. Reflection over that line
20.
Multiple Choice
(2 pts)
Which shape has exactly one line of symmetry and no rotational symmetry (other than a full turn)?
✓ Answer
A. Isosceles triangle
21.
Fill in the Blank
(2 pts)
The smallest angle that maps a square onto itself is _____ degrees.
22.
Fill in the Blank
(2 pts)
A figure that looks unchanged after a half-turn has rotational symmetry of order _____.
23.
Fill in the Blank
(2 pts)
An equilateral triangle has _____ lines of symmetry.
24.
Fill in the Blank
(2 pts)
A regular n-gon has _____ lines of symmetry.
25.
Fill in the Blank
(2 pts)
Reflecting a shape across its line of symmetry produces two _____ halves.
26.
Fill in the Blank
(2 pts)
A circle has an _____ number of lines of symmetry.
27.
Fill in the Blank
(2 pts)
The angle between adjacent spokes in a 12-spoke wheel is _____ degrees.
28.
Fill in the Blank
(2 pts)
A generic parallelogram (not a rectangle or rhombus) has _____ line(s) of symmetry.
29.
Fill in the Blank
(2 pts)
The smallest angle of rotation for a regular pentagon is _____.
30.
Fill in the Blank
(2 pts)
Folding along a line of symmetry makes the two sides _____.
31.
Word Problem
(5 pts)
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.
✎ 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.
Word Problem
(5 pts)
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.
✎ 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.
Word Problem
(5 pts)
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.
✎ 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.
Word Problem
(5 pts)
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.
✎ 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.
Word Problem
(5 pts)
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.
✎ 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.
Word Problem
(5 pts)
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.
✎ 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.
Word Problem
(5 pts)
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.
✎ 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.
Word Problem
(5 pts)
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.
✎ 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.
Word Problem
(5 pts)
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.
✎ 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.
Word Problem
(5 pts)
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.
✎ 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°.