{
  "Id": "7ad6ff2a-15b0-4cdf-b1de-45df460683b9",
  "Title": "Symmetry and Reflection Worksheet",
  "Subject": "Mathematics",
  "Topic": "Symmetry and Geometric Reflection",
  "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": "Ch14N.pdf",
  "SessionMaterialId": "dabc4d88-0d65-4aa2-a67b-96e96e40c20a",
  "GeneratedAt": "2026-05-31T13:44:21.163281Z",
  "Questions": [
    {
      "Id": 1,
      "Type": "true_false",
      "Text": "The angle of symmetry of every figure is always 360\u00B0.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 2,
      "Type": "true_false",
      "Text": "A square always has more lines of symmetry than a rectangle.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 3,
      "Type": "true_false",
      "Text": "An isosceles triangle has exactly 2 lines of symmetry.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 4,
      "Type": "true_false",
      "Text": "The letter H has both vertical and horizontal lines of symmetry.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 5,
      "Type": "true_false",
      "Text": "A butterfly can exhibit symmetry even if it appears to have only one wing.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 6,
      "Type": "true_false",
      "Text": "All regular pentagons have multiple lines of symmetry.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 7,
      "Type": "true_false",
      "Text": "Circles have an infinite number of lines of symmetry.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 8,
      "Type": "true_false",
      "Text": "An isosceles triangle has exactly one line of symmetry.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 9,
      "Type": "true_false",
      "Text": "Scalene triangles have at least one line of symmetry.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 10,
      "Type": "true_false",
      "Text": "A regular hexagon can have multiple lines of symmetry.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 11,
      "Type": "multiple_choice",
      "Text": "How many lines of symmetry are there in a rectangle?",
      "Options": [
        "A. 1",
        "B. 2",
        "C. 0",
        "D. 4"
      ],
      "Answer": "B. 2",
      "Points": 2
    },
    {
      "Id": 12,
      "Type": "multiple_choice",
      "Text": "Which of the following does not have any lines of symmetry?",
      "Options": [
        "A. Square",
        "B. Circle",
        "C. Scalene Triangle",
        "D. Equilateral Triangle"
      ],
      "Answer": "C. Scalene Triangle",
      "Points": 2
    },
    {
      "Id": 13,
      "Type": "multiple_choice",
      "Text": "Which of the following has two lines of symmetry?",
      "Options": [
        "A. Rectangle",
        "B. Square",
        "C. Parallelogram",
        "D. Triangle"
      ],
      "Answer": "A. Rectangle",
      "Points": 2
    },
    {
      "Id": 14,
      "Type": "multiple_choice",
      "Text": "Which letter is known to have both vertical and horizontal lines of symmetry?",
      "Options": [
        "A. X",
        "B. Z",
        "C. T",
        "D. F"
      ],
      "Answer": "A. X",
      "Points": 2
    },
    {
      "Id": 15,
      "Type": "multiple_choice",
      "Text": "How many lines of symmetry are there in an isosceles triangle?",
      "Options": [
        "A. 1",
        "B. 2",
        "C. 3",
        "D. 0"
      ],
      "Answer": "A. 1",
      "Points": 2
    },
    {
      "Id": 16,
      "Type": "multiple_choice",
      "Text": "Which type of symmetry is most commonly observed for the letter C?",
      "Options": [
        "A. Vertical",
        "B. Horizontal",
        "C. Rotational",
        "D. None"
      ],
      "Answer": "B. Horizontal",
      "Points": 2
    },
    {
      "Id": 17,
      "Type": "multiple_choice",
      "Text": "A regular pentagon has how many lines of symmetry?",
      "Options": [
        "A. 5",
        "B. 2",
        "C. 1",
        "D. 0"
      ],
      "Answer": "A. 5",
      "Points": 2
    },
    {
      "Id": 18,
      "Type": "multiple_choice",
      "Text": "An infinite number of lines of symmetry can be drawn in which shape?",
      "Options": [
        "A. Square",
        "B. Circle",
        "C. Triangle",
        "D. Pentagon"
      ],
      "Answer": "B. Circle",
      "Points": 2
    },
    {
      "Id": 19,
      "Type": "multiple_choice",
      "Text": "Which shape typically has an order of rotational symmetry equal to 2?",
      "Options": [
        "A. Equilateral Triangle",
        "B. Rectangle",
        "C. Regular Pentagon",
        "D. Circle"
      ],
      "Answer": "B. Rectangle",
      "Points": 2
    },
    {
      "Id": 20,
      "Type": "multiple_choice",
      "Text": "What is the main characteristic of reflection symmetry?",
      "Options": [
        "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",
      "Points": 2
    },
    {
      "Id": 21,
      "Type": "fill_blank",
      "Text": "_____ letters in the English alphabet look the same after a half turn (180 degrees).",
      "Options": [],
      "Answer": "some",
      "Points": 2
    },
    {
      "Id": 22,
      "Type": "fill_blank",
      "Text": "All rectangles have an order of rotational symmetry of _____.",
      "Options": [],
      "Answer": "2",
      "Points": 2
    },
    {
      "Id": 23,
      "Type": "fill_blank",
      "Text": "All squares have an order of rotational symmetry of _____.",
      "Options": [],
      "Answer": "4",
      "Points": 2
    },
    {
      "Id": 24,
      "Type": "fill_blank",
      "Text": "The order of rotational symmetry of an equilateral triangle is _____.",
      "Options": [],
      "Answer": "3",
      "Points": 2
    },
    {
      "Id": 25,
      "Type": "fill_blank",
      "Text": "A scalene triangle has _____ lines of symmetry.",
      "Options": [],
      "Answer": "0",
      "Points": 2
    },
    {
      "Id": 26,
      "Type": "fill_blank",
      "Text": "An isosceles triangle has _____ line of symmetry.",
      "Options": [],
      "Answer": "1",
      "Points": 2
    },
    {
      "Id": 27,
      "Type": "fill_blank",
      "Text": "A regular pentagon has _____ lines of symmetry.",
      "Options": [],
      "Answer": "5",
      "Points": 2
    },
    {
      "Id": 28,
      "Type": "fill_blank",
      "Text": "A circle has an infinite number of lines of symmetry, which can be described as _____.",
      "Options": [],
      "Answer": "infinite",
      "Points": 2
    },
    {
      "Id": 29,
      "Type": "fill_blank",
      "Text": "The butterfly\u0027s wings are _____.",
      "Options": [],
      "Answer": "symmetrical",
      "Points": 2
    },
    {
      "Id": 30,
      "Type": "fill_blank",
      "Text": "Reflection symmetry means that one side is the _____ image of the other.",
      "Options": [],
      "Answer": "mirror",
      "Points": 2
    },
    {
      "Id": 31,
      "Type": "word_problem",
      "Text": "A rectangle has 2 lines of symmetry. If a pattern repeats every 180\u00B0 rotation, how many times will it repeat in a full 360\u00B0 rotation? Show your working.",
      "Options": [],
      "Answer": "Step 1: Recognize that a 360\u00B0 rotation divided by 180\u00B0 equals 2.\nStep 2: Therefore, the pattern repeats 2 times in a full rotation.\nAnswer: 2",
      "Points": 5
    },
    {
      "Id": 32,
      "Type": "word_problem",
      "Text": "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.",
      "Options": [],
      "Answer": "Step 1: Identify the vertical, horizontal, and two diagonal lines.\nStep 2: Total reflective symmetries = 4.\nAnswer: 4",
      "Points": 5
    },
    {
      "Id": 33,
      "Type": "word_problem",
      "Text": "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.",
      "Options": [],
      "Answer": "Step 1: Divide 360\u00B0 by the order 3.\nStep 2: 360\u00B0 / 3 = 120\u00B0.\nAnswer: 120\u00B0",
      "Points": 5
    },
    {
      "Id": 34,
      "Type": "word_problem",
      "Text": "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.",
      "Options": [],
      "Answer": "Step 1: Recognize that drawing any finite number of lines does not change the inherent properties of a circle.\nStep 2: The circle still has infinite lines of symmetry.\nAnswer: No, the circle retains infinite symmetry.",
      "Points": 5
    },
    {
      "Id": 35,
      "Type": "word_problem",
      "Text": "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.",
      "Options": [],
      "Answer": "Step 1: Note that a square has 4 lines and a rectangle has 2 lines.\nStep 2: Factor = 4 / 2 = 2.\nAnswer: 2",
      "Points": 5
    },
    {
      "Id": 36,
      "Type": "word_problem",
      "Text": "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.",
      "Options": [],
      "Answer": "Step 1: Isosceles triangle lines = 1, Scalene triangle lines = 0.\nStep 2: Difference = 1 - 0 = 1.\nAnswer: 1",
      "Points": 5
    },
    {
      "Id": 37,
      "Type": "word_problem",
      "Text": "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.",
      "Options": [],
      "Answer": "Step 1: Regular pentagon has 5 lines of symmetry.\nStep 2: Its rotational symmetry order is also 5.\nStep 3: Sum = 5 \u002B 5 = 10.\nAnswer: 10",
      "Points": 5
    },
    {
      "Id": 38,
      "Type": "word_problem",
      "Text": "Consider a butterfly with 2 lines of symmetry. If one wing is folded over, how many lines of symmetry remain visible? Show your working.",
      "Options": [],
      "Answer": "Step 1: Originally, the butterfly has 2 lines of symmetry.\nStep 2: Folding one wing typically reveals only the vertical line of symmetry.\nAnswer: 1",
      "Points": 5
    },
    {
      "Id": 39,
      "Type": "word_problem",
      "Text": "If the word \u0027SYMMETRY\u0027 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.",
      "Options": [],
      "Answer": "Step 1: Average symmetry lines per letter = 1.\nStep 2: Total letters = 8.\nStep 3: Total symmetry lines = 1 x 8 = 8.\nAnswer: 8",
      "Points": 5
    },
    {
      "Id": 40,
      "Type": "word_problem",
      "Text": "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.",
      "Options": [],
      "Answer": "Step 1: Drawing all 6 lines of symmetry in a regular hexagon divides it into multiple regions.\nStep 2: The intersecting lines create 12 congruent regions.\nAnswer: 12",
      "Points": 5
    }
  ],
  "TotalPoints": 100
}