{
  "Id": "9068593f-35b9-4d49-aef2-582775d70fb8",
  "Title": "Class 6 Mathematics \u2014 Symmetry: Lines and Rotations",
  "Subject": "Mathematics",
  "Topic": "Symmetry (Lines of Symmetry and Rotational Symmetry)",
  "Instructions": "Read each question carefully and answer to the best of your ability. Show all working for word problems.",
  "EstimatedMinutes": 35,
  "StudentProfileId": "dd186faa-f489-46ee-84e4-26e2d01e2691",
  "SourceFileName": "math-symmetry.pdf",
  "SessionMaterialId": "476616bb-1280-4378-9bfe-32ba2eb61f45",
  "GeneratedAt": "2026-08-16T10:27:53.708429Z",
  "Questions": [
    {
      "Id": 1,
      "Type": "true_false",
      "Text": "A scalene triangle has no line of symmetry.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 2,
      "Type": "true_false",
      "Text": "A rectangle has exactly one line of symmetry.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 3,
      "Type": "true_false",
      "Text": "A regular hexagon has rotational symmetry of order 6.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 4,
      "Type": "true_false",
      "Text": "A kite always has two lines of symmetry.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 5,
      "Type": "true_false",
      "Text": "A circle has rotational symmetry for every angle of rotation.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 6,
      "Type": "true_false",
      "Text": "A generic parallelogram (that is not a rectangle or rhombus) has no line of symmetry.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 7,
      "Type": "true_false",
      "Text": "Folding a figure along one of its lines of symmetry will make the two halves coincide.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 8,
      "Type": "true_false",
      "Text": "The smallest angle of rotation for a regular pentagon is 60\u00B0.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 9,
      "Type": "true_false",
      "Text": "An equilateral triangle has exactly two lines of symmetry.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 10,
      "Type": "true_false",
      "Text": "The uppercase letters M and W (in standard block style) have the same number of lines of symmetry.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 11,
      "Type": "multiple_choice",
      "Text": "Which shape has no line of symmetry but has rotational symmetry of order 2?",
      "Options": [
        "A. Rectangle",
        "B. Rhombus",
        "C. Parallelogram (not a rectangle)",
        "D. Isosceles trapezium"
      ],
      "Answer": "C. Parallelogram (not a rectangle)",
      "Points": 2
    },
    {
      "Id": 12,
      "Type": "multiple_choice",
      "Text": "What is the smallest angle that maps a regular octagon to itself?",
      "Options": [
        "A. 36\u00B0",
        "B. 45\u00B0",
        "C. 60\u00B0",
        "D. 90\u00B0"
      ],
      "Answer": "B. 45\u00B0",
      "Points": 2
    },
    {
      "Id": 13,
      "Type": "multiple_choice",
      "Text": "How many lines of symmetry does a regular five-pointed star (pentagram) have?",
      "Options": [
        "A. 0",
        "B. 2",
        "C. 5",
        "D. 10"
      ],
      "Answer": "C. 5",
      "Points": 2
    },
    {
      "Id": 14,
      "Type": "multiple_choice",
      "Text": "An isosceles triangle with a horizontal base has which line of symmetry?",
      "Options": [
        "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",
      "Points": 2
    },
    {
      "Id": 15,
      "Type": "multiple_choice",
      "Text": "What is the order of rotational symmetry of a square?",
      "Options": [
        "A. 1",
        "B. 2",
        "C. 3",
        "D. 4"
      ],
      "Answer": "D. 4",
      "Points": 2
    },
    {
      "Id": 16,
      "Type": "multiple_choice",
      "Text": "How many lines of symmetry does a regular dodecagon have?",
      "Options": [
        "A. 6",
        "B. 8",
        "C. 10",
        "D. 12"
      ],
      "Answer": "D. 12",
      "Points": 2
    },
    {
      "Id": 17,
      "Type": "multiple_choice",
      "Text": "If the smallest angle of rotation for a figure is 120\u00B0, what is the order of its rotational symmetry?",
      "Options": [
        "A. 2",
        "B. 3",
        "C. 4",
        "D. 6"
      ],
      "Answer": "B. 3",
      "Points": 2
    },
    {
      "Id": 18,
      "Type": "multiple_choice",
      "Text": "Which statement is true for a rhombus that is not a square?",
      "Options": [
        "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.",
      "Points": 2
    },
    {
      "Id": 19,
      "Type": "multiple_choice",
      "Text": "Which transformation makes a figure coincide with itself across a symmetry line?",
      "Options": [
        "A. Translation",
        "B. Reflection over that line",
        "C. Rotation about a corner",
        "D. Enlargement"
      ],
      "Answer": "B. Reflection over that line",
      "Points": 2
    },
    {
      "Id": 20,
      "Type": "multiple_choice",
      "Text": "Which shape has exactly one line of symmetry and no rotational symmetry (other than a full turn)?",
      "Options": [
        "A. Isosceles triangle",
        "B. Rectangle",
        "C. Regular hexagon",
        "D. Scalene triangle"
      ],
      "Answer": "A. Isosceles triangle",
      "Points": 2
    },
    {
      "Id": 21,
      "Type": "fill_blank",
      "Text": "The smallest angle that maps a square onto itself is _____ degrees.",
      "Options": [],
      "Answer": "90\u00B0",
      "Points": 2
    },
    {
      "Id": 22,
      "Type": "fill_blank",
      "Text": "A figure that looks unchanged after a half-turn has rotational symmetry of order _____.",
      "Options": [],
      "Answer": "2",
      "Points": 2
    },
    {
      "Id": 23,
      "Type": "fill_blank",
      "Text": "An equilateral triangle has _____ lines of symmetry.",
      "Options": [],
      "Answer": "3",
      "Points": 2
    },
    {
      "Id": 24,
      "Type": "fill_blank",
      "Text": "A regular n-gon has _____ lines of symmetry.",
      "Options": [],
      "Answer": "n",
      "Points": 2
    },
    {
      "Id": 25,
      "Type": "fill_blank",
      "Text": "Reflecting a shape across its line of symmetry produces two _____ halves.",
      "Options": [],
      "Answer": "congruent",
      "Points": 2
    },
    {
      "Id": 26,
      "Type": "fill_blank",
      "Text": "A circle has an _____ number of lines of symmetry.",
      "Options": [],
      "Answer": "infinite",
      "Points": 2
    },
    {
      "Id": 27,
      "Type": "fill_blank",
      "Text": "The angle between adjacent spokes in a 12-spoke wheel is _____ degrees.",
      "Options": [],
      "Answer": "30\u00B0",
      "Points": 2
    },
    {
      "Id": 28,
      "Type": "fill_blank",
      "Text": "A generic parallelogram (not a rectangle or rhombus) has _____ line(s) of symmetry.",
      "Options": [],
      "Answer": "0",
      "Points": 2
    },
    {
      "Id": 29,
      "Type": "fill_blank",
      "Text": "The smallest angle of rotation for a regular pentagon is _____.",
      "Options": [],
      "Answer": "72\u00B0",
      "Points": 2
    },
    {
      "Id": 30,
      "Type": "fill_blank",
      "Text": "Folding along a line of symmetry makes the two sides _____.",
      "Options": [],
      "Answer": "coincide",
      "Points": 2
    },
    {
      "Id": 31,
      "Type": "word_problem",
      "Text": "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.",
      "Options": [],
      "Answer": "Step 1: Identify number of repeated parts n = 8.\nStep 2: Order of rotational symmetry = n = 8.\nStep 3: Smallest angle = 360\u00B0 \u00F7 n = 360\u00B0 \u00F7 8 = 45\u00B0.\nAnswer: Order 8; smallest angle 45\u00B0.",
      "Points": 5
    },
    {
      "Id": 32,
      "Type": "word_problem",
      "Text": "A regular polygon has each interior angle measuring 140\u00B0. Find (a) the number of sides, (b) the number of lines of symmetry, and (c) the smallest angle of rotation. Show your working.",
      "Options": [],
      "Answer": "Step 1: Use interior angle formula: ((n \u2212 2) \u00D7 180\u00B0) \u00F7 n = 140\u00B0.\nStep 2: 180n \u2212 360 = 140n \u21D2 40n = 360 \u21D2 n = 9.\nStep 3: Lines of symmetry for a regular n-gon = n = 9.\nStep 4: Smallest angle of rotation = 360\u00B0 \u00F7 n = 360\u00B0 \u00F7 9 = 40\u00B0.\nAnswer: (a) 9 sides, (b) 9 lines of symmetry, (c) 40\u00B0.",
      "Points": 5
    },
    {
      "Id": 33,
      "Type": "word_problem",
      "Text": "A pattern looks the same after a rotation of 24\u00B0. How many distinct orientations will it have in one full turn, and what is its order of rotational symmetry? Show your working.",
      "Options": [],
      "Answer": "Step 1: Number of repeats in a full turn = 360\u00B0 \u00F7 24\u00B0.\nStep 2: 360 \u00F7 24 = 15.\nStep 3: Order of rotational symmetry equals the number of repeats = 15.\nAnswer: 15 distinct orientations; order 15.",
      "Points": 5
    },
    {
      "Id": 34,
      "Type": "word_problem",
      "Text": "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.",
      "Options": [],
      "Answer": "Step 1: Smallest angle = 360\u00B0 \u00F7 number of spokes = 360\u00B0 \u00F7 18 = 20\u00B0.\nStep 2: The order of rotational symmetry equals the number of spokes = 18.\nAnswer: (a) 20\u00B0, (b) 18 rotational symmetries.",
      "Points": 5
    },
    {
      "Id": 35,
      "Type": "word_problem",
      "Text": "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.",
      "Options": [],
      "Answer": "Step 1: Count repeated features: n = 10.\nStep 2: Order of rotational symmetry = n = 10.\nStep 3: Smallest angle = 360\u00B0 \u00F7 10 = 36\u00B0.\nStep 4: For an evenly spaced, regular arrangement, lines of symmetry = n = 10.\nAnswer: (a) Order 10, (b) 36\u00B0, (c) 10 lines of symmetry.",
      "Points": 5
    },
    {
      "Id": 36,
      "Type": "word_problem",
      "Text": "A designer wants a logo that repeats perfectly after every 30\u00B0 turn. (a) How many identical sectors will the logo have? (b) What is its rotational symmetry order? Show your working.",
      "Options": [],
      "Answer": "Step 1: Number of sectors = 360\u00B0 \u00F7 30\u00B0 = 12.\nStep 2: Order of rotational symmetry equals number of sectors = 12.\nAnswer: (a) 12 sectors, (b) order 12.",
      "Points": 5
    },
    {
      "Id": 37,
      "Type": "word_problem",
      "Text": "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.",
      "Options": [],
      "Answer": "Step 1: Folding along a symmetry line creates mirror points on reopening.\nStep 2: One punch through two layers produces two holes symmetric about the fold.\nStep 3: Distances from the fold are equal to the original 3 cm on each side.\nAnswer: Two holes; one 3 cm to the right and one 3 cm to the left of the fold.",
      "Points": 5
    },
    {
      "Id": 38,
      "Type": "word_problem",
      "Text": "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.",
      "Options": [],
      "Answer": "Step 1: Angle per step = 360\u00B0 \u00F7 order = 360\u00B0 \u00F7 9 = 40\u00B0.\nStep 2: For a regular polygon, lines of symmetry = number of sides = order = 9.\nAnswer: (a) 40\u00B0, (b) 9 lines of symmetry.",
      "Points": 5
    },
    {
      "Id": 39,
      "Type": "word_problem",
      "Text": "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.",
      "Options": [],
      "Answer": "Step 1: With 12 identical, evenly spaced marks, n = 12.\nStep 2: Order of rotational symmetry = n = 12.\nStep 3: Smallest rotation = 360\u00B0 \u00F7 12 = 30\u00B0.\nAnswer: (a) Order 12, (b) 30\u00B0.",
      "Points": 5
    },
    {
      "Id": 40,
      "Type": "word_problem",
      "Text": "Each interior angle of a regular polygon is 165\u00B0. Find (a) the number of sides, (b) the number of lines of symmetry, and (c) the smallest angle of rotation. Show your working.",
      "Options": [],
      "Answer": "Step 1: Use ((n \u2212 2) \u00D7 180\u00B0) \u00F7 n = 165\u00B0.\nStep 2: 180n \u2212 360 = 165n \u21D2 15n = 360 \u21D2 n = 24.\nStep 3: Lines of symmetry for a regular n-gon = n = 24.\nStep 4: Smallest angle of rotation = 360\u00B0 \u00F7 24 = 15\u00B0.\nAnswer: (a) 24 sides, (b) 24 lines of symmetry, (c) 15\u00B0.",
      "Points": 5
    }
  ],
  "TotalPoints": 100
}