[
  {
    "Question": "What is the Pythagorean theorem?",
    "Answer": "A",
    "Explanation": "The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.",
    "PictureURL": "",
    "OptionA": "a² + b² = c²",
    "OptionB": "a² - b² = c²",
    "OptionC": "a + b = c",
    "OptionD": "a² + b² = 2c",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Geometry Practice Test",
    "Content Type": "Mathematics",
    "Title": "Pythagorean Theorem Basics",
    "Item": 1,
    "Type": "multiple choice",
    "Path": "geometry/pythagorean_theorem"
  },
  {
    "Question": "If one leg of a right triangle is 3 units and the other leg is 4 units, what is the length of the hypotenuse?",
    "Answer": "B",
    "Explanation": "Using the Pythagorean theorem: c² = 3² + 4² = 9 + 16 = 25, so c = √25 = 5.",
    "PictureURL": "",
    "OptionA": "4",
    "OptionB": "5",
    "OptionC": "6",
    "OptionD": "7",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Geometry Practice Test",
    "Content Type": "Mathematics",
    "Title": "Finding the Hypotenuse",
    "Item": 2,
    "Type": "multiple choice",
    "Path": "geometry/pythagorean_theorem"
  },
  {
    "Question": "In a right triangle, if the hypotenuse is 10 units and one leg is 6 units, what is the length of the other leg?",
    "Answer": "C",
    "Explanation": "Using the Pythagorean theorem: c² = a² + b², so 10² = 6² + b². This gives 100 = 36 + b², thus b² = 64, and b = 8.",
    "PictureURL": "",
    "OptionA": "6",
    "OptionB": "7",
    "OptionC": "8",
    "OptionD": "9",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Geometry Practice Test",
    "Content Type": "Mathematics",
    "Title": "Finding a Leg of the Triangle",
    "Item": 3,
    "Type": "multiple choice",
    "Path": "geometry/pythagorean_theorem"
  },
  {
    "Question": "Which of the following triangles is a right triangle?",
    "Answer": "A",
    "Explanation": "A triangle with sides 5, 12, and 13 satisfies the Pythagorean theorem: 5² + 12² = 13², or 25 + 144 = 169.",
    "PictureURL": "",
    "OptionA": "5, 12, 13",
    "OptionB": "6, 8, 10",
    "OptionC": "7, 24, 25",
    "OptionD": "3, 4, 5",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Geometry Practice Test",
    "Content Type": "Mathematics",
    "Title": "Identifying Right Triangles",
    "Item": 4,
    "Type": "multiple choice",
    "Path": "geometry/pythagorean_theorem"
  },
  {
    "Question": "What is the distance between the points (1, 2) and (4, 6) in a coordinate plane?",
    "Answer": "D",
    "Explanation": "Using the distance formula derived from the Pythagorean theorem: d = √((4-1)² + (6-2)²) = √(3² + 4²) = √(9 + 16) = √25 = 5.",
    "PictureURL": "",
    "OptionA": "3",
    "OptionB": "4",
    "OptionC": "5",
    "OptionD": "5",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Geometry Practice Test",
    "Content Type": "Mathematics",
    "Title": "Distance Between Points",
    "Item": 5,
    "Type": "multiple choice",
    "Path": "geometry/pythagorean_theorem"
  },
  {
    "Question": "If a ladder is leaning against a wall and reaches a height of 8 feet while the base is 6 feet away from the wall, how long is the ladder?",
    "Answer": "B",
    "Explanation": "Using the Pythagorean theorem: c² = 8² + 6² = 64 + 36 = 100, so c = √100 = 10 feet.",
    "PictureURL": "",
    "OptionA": "8",
    "OptionB": "10",
    "OptionC": "12",
    "OptionD": "14",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Geometry Practice Test",
    "Content Type": "Mathematics",
    "Title": "Length of the Ladder",
    "Item": 6,
    "Type": "multiple choice",
    "Path": "geometry/pythagorean_theorem"
  },
  {
    "Question": "What is the area of a right triangle with legs measuring 5 units and 12 units?",
    "Answer": "C",
    "Explanation": "The area of a right triangle is given by (1/2) * base * height. Here, Area = (1/2) * 5 * 12 = 30 square units.",
    "PictureURL": "",
    "OptionA": "20",
    "OptionB": "25",
    "OptionC": "30",
    "OptionD": "35",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Geometry Practice Test",
    "Content Type": "Mathematics",
    "Title": "Area of a Right Triangle",
    "Item": 7,
    "Type": "multiple choice",
    "Path": "geometry/pythagorean_theorem"
  },
  {
    "Question": "In a right triangle, if the lengths of the legs are equal, what type of triangle is it?",
    "Answer": "A",
    "Explanation": "If the lengths of the legs are equal, it is an isosceles right triangle, where the angles opposite the equal sides are both 45 degrees.",
    "PictureURL": "",
    "OptionA": "Isosceles right triangle",
    "OptionB": "Equilateral triangle",
    "OptionC": "Scalene triangle",
    "OptionD": "Obtuse triangle",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Geometry Practice Test",
    "Content Type": "Mathematics",
    "Title": "Types of Right Triangles",
    "Item": 8,
    "Type": "multiple choice",
    "Path": "geometry/pythagorean_theorem"
  },
  {
    "Question": "What is the length of the diagonal of a rectangle with a width of 6 units and a height of 8 units?",
    "Answer": "D",
    "Explanation": "Using the Pythagorean theorem: d² = 6² + 8² = 36 + 64 = 100, so d = √100 = 10 units.",
    "PictureURL": "",
    "OptionA": "8",
    "OptionB": "9",
    "OptionC": "11",
    "OptionD": "10",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Geometry Practice Test",
    "Content Type": "Mathematics",
    "Title": "Diagonal of a Rectangle",
    "Item": 9,
    "Type": "multiple choice",
    "Path": "geometry/pythagorean_theorem"
  },
  {
    "Question": "If a right triangle has a hypotenuse of 15 units and one leg of 9 units, what is the length of the other leg?",
    "Answer": "C",
    "Explanation": "Using the Pythagorean theorem: 15² = 9² + b², so 225 = 81 + b², thus b² = 144, and b = 12.",
    "PictureURL": "",
    "OptionA": "10",
    "OptionB": "11",
    "OptionC": "12",
    "OptionD": "13",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Geometry Practice Test",
    "Content Type": "Mathematics",
    "Title": "Finding the Other Leg",
    "Item": 10,
    "Type": "multiple choice",
    "Path": "geometry/pythagorean_theorem"
  },
  {
    "Question": "What is the relationship between the sides of a 30-60-90 triangle?",
    "Answer": "B",
    "Explanation": "In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2, where the side opposite the 30-degree angle is the shortest.",
    "PictureURL": "",
    "OptionA": "1:1:1",
    "OptionB": "1:√3:2",
    "OptionC": "1:2:√3",
    "OptionD": "1:2:1",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Geometry Practice Test",
    "Content Type": "Mathematics",
    "Title": "30-60-90 Triangle Ratios",
    "Item": 11,
    "Type": "multiple choice",
    "Path": "geometry/pythagorean_theorem"
  },
  {
    "Question": "What is the length of the hypotenuse in a right triangle with legs measuring 7 units and 24 units?",
    "Answer": "A",
    "Explanation": "Using the Pythagorean theorem: c² = 7² + 24² = 49 + 576 = 625, so c = √625 = 25.",
    "PictureURL": "",
    "OptionA": "25",
    "OptionB": "26",
    "OptionC": "27",
    "OptionD": "28",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Geometry Practice Test",
    "Content Type": "Mathematics",
    "Title": "Hypotenuse Length Calculation",
    "Item": 12,
    "Type": "multiple choice",
    "Path": "geometry/pythagorean_theorem"
  },
  {
    "Question": "In a right triangle, if the hypotenuse is 13 units and one leg is 5 units, what is the length of the other leg?",
    "Answer": "D",
    "Explanation": "Using the Pythagorean theorem: 13² = 5² + b², so 169 = 25 + b², thus b² = 144, and b = 12.",
    "PictureURL": "",
    "OptionA": "10",
    "OptionB": "11",
    "OptionC": "12",
    "OptionD": "12",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Geometry Practice Test",
    "Content Type": "Mathematics",
    "Title": "Finding the Missing Leg",
    "Item": 13,
    "Type": "multiple choice",
    "Path": "geometry/pythagorean_theorem"
  },
  {
    "Question": "What is the perimeter of a right triangle with legs measuring 9 units and 12 units?",
    "Answer": "C",
    "Explanation": "First, find the hypotenuse using the Pythagorean theorem: c² = 9² + 12² = 81 + 144 = 225, so c = 15. The perimeter is 9 + 12 + 15 = 36 units.",
    "PictureURL": "",
    "OptionA": "30",
    "OptionB": "32",
    "OptionC": "36",
    "OptionD": "38",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Geometry Practice Test",
    "Content Type": "Mathematics",
    "Title": "Perimeter of a Right Triangle",
    "Item": 14,
    "Type": "multiple choice",
    "Path": "geometry/pythagorean_theorem"
  },
  {
    "Question": "What is the length of the hypotenuse of a right triangle with legs measuring 8 units and 15 units?",
    "Answer": "B",
    "Explanation": "Using the Pythagorean theorem: c² = 8² + 15² = 64 + 225 = 289, so c = √289 = 17.",
    "PictureURL": "",
    "OptionA": "16",
    "OptionB": "17",
    "OptionC": "18",
    "OptionD": "19",
    "OptionE": "",
    "OptionF": "",
    "OptionG": "",
    "TestName": "Geometry Practice Test",
    "Content Type": "Mathematics",
    "Title": "Hypotenuse Length Calculation",
    "Item": 15,
    "Type": "multiple choice",
    "Path": "geometry/pythagorean_theorem"
  }
]