{
  "title": "Construction of Triangles - Grade 7 ICSE",
  "total_questions": 60,
  "questions": [
    {
      "id": 1,
      "difficulty": "easy",
      "question": "What instrument is used to draw arcs in triangle construction? 🌀",
      "options": {
        "A": "Ruler",
        "B": "Protractor",
        "C": "Compass",
        "D": "Set square"
      },
      "correct_answer": "C"
    },
    {
      "id": 2,
      "difficulty": "easy",
      "question": "To construct a triangle with sides 5 cm, 6 cm, 7 cm, which criterion is used? 📏",
      "options": { "A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS" },
      "correct_answer": "A"
    },
    {
      "id": 3,
      "difficulty": "easy",
      "question": "Which triangle cannot be constructed? 🚫",
      "options": {
        "A": "Sides 3,4,5 cm",
        "B": "Sides 2,3,6 cm",
        "C": "Sides 5,5,5 cm",
        "D": "Sides 4,5,6 cm"
      },
      "correct_answer": "B"
    },
    {
      "id": 4,
      "difficulty": "easy",
      "question": "The sum of any two sides of a triangle must be ______ the third side. ➕",
      "options": {
        "A": "less than",
        "B": "greater than",
        "C": "equal to",
        "D": "half of"
      },
      "correct_answer": "B"
    },
    {
      "id": 5,
      "difficulty": "easy",
      "question": "To construct ΔABC with AB=5cm, ∠A=60°, AC=4cm, we use: 🔺",
      "options": { "A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS" },
      "correct_answer": "B"
    },
    {
      "id": 6,
      "difficulty": "easy",
      "question": "Which angle is drawn first in SAS construction? 📐",
      "options": {
        "A": "Included angle",
        "B": "Right angle",
        "C": "Smallest angle",
        "D": "Largest angle"
      },
      "correct_answer": "A"
    },
    {
      "id": 7,
      "difficulty": "easy",
      "question": "A triangle with sides 2 cm, 3 cm, 5 cm is: 🤔",
      "options": {
        "A": "possible",
        "B": "impossible",
        "C": "right-angled",
        "D": "equilateral"
      },
      "correct_answer": "B"
    },
    {
      "id": 8,
      "difficulty": "easy",
      "question": "For ASA construction, we need: 🧩",
      "options": {
        "A": "two sides and included angle",
        "B": "two angles and included side",
        "C": "three sides",
        "D": "right angle and hypotenuse"
      },
      "correct_answer": "B"
    },
    {
      "id": 9,
      "difficulty": "easy",
      "question": "To construct a right triangle with hypotenuse 10 cm and one leg 6 cm, we use: ⬜",
      "options": { "A": "SSS", "B": "SAS", "C": "RHS", "D": "ASA" },
      "correct_answer": "C"
    },
    {
      "id": 10,
      "difficulty": "easy",
      "question": "The first step in constructing any triangle is usually to draw: ✏️",
      "options": {
        "A": "an arc",
        "B": "a base line",
        "C": "an altitude",
        "D": "a circle"
      },
      "correct_answer": "B"
    },
    {
      "id": 11,
      "difficulty": "easy",
      "question": "Can we construct a triangle with angles 50°, 60°, 70°? 📐",
      "options": {
        "A": "Yes",
        "B": "No",
        "C": "Only with a ruler",
        "D": "Only with a protractor"
      },
      "correct_answer": "A"
    },
    {
      "id": 12,
      "difficulty": "easy",
      "question": "To measure an angle during construction, we use: 📏",
      "options": {
        "A": "Ruler",
        "B": "Compass",
        "C": "Protractor",
        "D": "Divider"
      },
      "correct_answer": "C"
    },
    {
      "id": 13,
      "difficulty": "easy",
      "question": "The triangle inequality states: 3 + 4 > ? for sides 3,4,5 cm. ➗",
      "options": { "A": "3", "B": "4", "C": "5", "D": "7" },
      "correct_answer": "C"
    },
    {
      "id": 14,
      "difficulty": "easy",
      "question": "Which triangle is always constructible? ✅",
      "options": {
        "A": "Sides 1,2,4 cm",
        "B": "Sides 3,4,8 cm",
        "C": "Sides 6,7,8 cm",
        "D": "Sides 2,3,6 cm"
      },
      "correct_answer": "C"
    },
    {
      "id": 15,
      "difficulty": "easy",
      "question": "In RHS construction, we start by drawing: 🎯",
      "options": {
        "A": "the hypotenuse (given side)",
        "B": "the right angle first",
        "C": "the perpendicular bisector",
        "D": "an angle bisector"
      },
      "correct_answer": "A"
    },
    {
      "id": 16,
      "difficulty": "easy",
      "question": "An equilateral triangle of side 5 cm is constructed using: 🔺",
      "options": { "A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS" },
      "correct_answer": "A"
    },
    {
      "id": 17,
      "difficulty": "easy",
      "question": "If two angles of a triangle are 40° and 60°, the third angle is: 🔢",
      "options": { "A": "60°", "B": "70°", "C": "80°", "D": "90°" },
      "correct_answer": "C"
    },
    {
      "id": 18,
      "difficulty": "easy",
      "question": "Can we construct a unique triangle with angles 30°, 60°, 90°? 🤔",
      "options": {
        "A": "Yes",
        "B": "No, infinite triangles",
        "C": "Only if one side is given",
        "D": "Never"
      },
      "correct_answer": "C"
    },
    {
      "id": 19,
      "difficulty": "easy",
      "question": "For SAS construction, the given angle is: 📍",
      "options": {
        "A": "between the given sides",
        "B": "opposite to a side",
        "C": "right angle",
        "D": "largest angle"
      },
      "correct_answer": "A"
    },
    {
      "id": 20,
      "difficulty": "easy",
      "question": "To construct an isosceles triangle with equal sides 5 cm and base 6 cm, use: 🏗️",
      "options": {
        "A": "SSS",
        "B": "SAS",
        "C": "ASA",
        "D": "RHS"
      },
      "correct_answer": "A"
    },
    {
      "id": 21,
      "difficulty": "medium",
      "question": "Construct ΔPQR with PQ=7cm, QR=6cm, PR=5cm. Which side should be drawn first? 🎯",
      "options": {
        "A": "PQ",
        "B": "QR",
        "C": "PR",
        "D": "Any side"
      },
      "correct_answer": "D"
    },
    {
      "id": 22,
      "difficulty": "medium",
      "question": "In constructing ΔABC with BC=8cm, ∠B=45°, AB=6cm, where do you draw the angle? 📐",
      "options": {
        "A": "At point A",
        "B": "At point B",
        "C": "At point C",
        "D": "Anywhere"
      },
      "correct_answer": "B"
    },
    {
      "id": 23,
      "difficulty": "medium",
      "question": "To construct ΔXYZ with ∠X=50°, XY=7cm, ∠Y=60°, we use: 🔧",
      "options": { "A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS" },
      "correct_answer": "C"
    },
    {
      "id": 24,
      "difficulty": "medium",
      "question": "Which set of measurements gives a unique triangle? 🎲",
      "options": {
        "A": "AB=5cm, BC=6cm, ∠C=50°",
        "B": "∠A=40°, ∠B=60°, ∠C=80°",
        "C": "AB=4cm, BC=3cm, CA=8cm",
        "D": "∠A=90°, BC=10cm, AC=6cm"
      },
      "correct_answer": "D"
    },
    {
      "id": 25,
      "difficulty": "medium",
      "question": "Construct a right ΔABC with ∠B=90°, BC=4cm, AC=5cm. What is AB? 📏",
      "options": { "A": "3 cm", "B": "4 cm", "C": "5 cm", "D": "6 cm" },
      "correct_answer": "A"
    },
    {
      "id": 26,
      "difficulty": "medium",
      "question": "If in ΔPQR, PQ=5cm, ∠P=60°, and PR=5cm, what type of triangle is it? 🔺",
      "options": {
        "A": "Scalene",
        "B": "Isosceles",
        "C": "Equilateral",
        "D": "Right"
      },
      "correct_answer": "C"
    },
    {
      "id": 27,
      "difficulty": "medium",
      "question": "To construct ΔABC with AB=6cm, AC=7cm, and altitude from A=5cm, how many triangles possible? 🤯",
      "options": {
        "A": "1",
        "B": "2",
        "C": "4",
        "D": "0"
      },
      "correct_answer": "B"
    },
    {
      "id": 28,
      "difficulty": "medium",
      "question": "Construct an isosceles triangle with base 8 cm and each base angle 55°. What is the vertex angle? 🧮",
      "options": { "A": "55°", "B": "70°", "C": "80°", "D": "90°" },
      "correct_answer": "B"
    },
    {
      "id": 29,
      "difficulty": "medium",
      "question": "Which measurements give exactly two possible triangles? 🔄",
      "options": { "A": "SSS", "B": "SAS", "C": "SSA", "D": "ASA" },
      "correct_answer": "C"
    },
    {
      "id": 30,
      "difficulty": "medium",
      "question": "In constructing ΔLMN with LM=5cm, ∠L=120°, LN=3cm, the triangle is: ⚠️",
      "options": {
        "A": "acute",
        "B": "obtuse",
        "C": "right",
        "D": "equilateral"
      },
      "correct_answer": "B"
    },
    {
      "id": 31,
      "difficulty": "medium",
      "question": "To construct ΔABC with perimeter 15cm, AB:BC:CA=2:3:4, what is BC? 📊",
      "options": { "A": "3 cm", "B": "5 cm", "C": "6 cm", "D": "7 cm" },
      "correct_answer": "B"
    },
    {
      "id": 32,
      "difficulty": "medium",
      "question": "Construct ΔPQR with ∠Q=90°, QR=3cm, PR=5cm. What is PQ? 🔍",
      "options": { "A": "3 cm", "B": "4 cm", "C": "5 cm", "D": "6 cm" },
      "correct_answer": "B"
    },
    {
      "id": 33,
      "difficulty": "medium",
      "question": "Can you construct ΔABC with AB=7cm, ∠A=100°, ∠B=30°? 🤔",
      "options": {
        "A": "Yes",
        "B": "No",
        "C": "Only if ∠C=50°",
        "D": "Only with compass"
      },
      "correct_answer": "A"
    },
    {
      "id": 34,
      "difficulty": "medium",
      "question": "In ΔXYZ, if XY=6cm, YZ=8cm, and ∠Y=90°, what is XZ? 📐",
      "options": { "A": "10 cm", "B": "12 cm", "C": "14 cm", "D": "16 cm" },
      "correct_answer": "A"
    },
    {
      "id": 35,
      "difficulty": "medium",
      "question": "Construct an equilateral triangle of altitude 5 cm. What is its side? 🏔️",
      "options": { "A": "5 cm", "B": "5.77 cm", "C": "6 cm", "D": "10 cm" },
      "correct_answer": "B"
    },
    {
      "id": 36,
      "difficulty": "medium",
      "question": "How many triangles can be constructed with sides 7cm, 5cm, and included angle 40°? 🔢",
      "options": { "A": "0", "B": "1", "C": "2", "D": "Infinite" },
      "correct_answer": "B"
    },
    {
      "id": 37,
      "difficulty": "medium",
      "question": "Construct ΔABC with BC=9cm, ∠B=45°, AB-AC=2cm. How many triangles possible? 🎯",
      "options": {
        "A": "0",
        "B": "1",
        "C": "2",
        "D": "3"
      },
      "correct_answer": "B"
    },
    {
      "id": 38,
      "difficulty": "medium",
      "question": "To construct a triangle similar to a given triangle with scale factor 2/3, we use: 📏",
      "options": { "A": "SSS", "B": "SAS", "C": "ASA", "D": "Any criterion" },
      "correct_answer": "D"
    },
    {
      "id": 39,
      "difficulty": "medium",
      "question": "Construct ΔPQR with ∠P=30°, ∠Q=60°, and perimeter 18cm. What is PQ+QR? 🔄",
      "options": {
        "A": "9 cm",
        "B": "27 - 9√3 cm",
        "C": "12 cm",
        "D": "15 cm"
      },
      "correct_answer": "B"
    },
    {
      "id": 40,
      "difficulty": "medium",
      "question": "Which triangle cannot be constructed? 🚫",
      "options": {
        "A": "Sides 4,5,6 cm, ∠ between 4&5=60°",
        "B": "∠A=50°, ∠B=60°, side AB=5cm",
        "C": "∠A=90°, BC=10cm, AC=12cm",
        "D": "Sides 2,3,7 cm"
      },
      "correct_answer": "D"
    },
    {
      "id": 41,
      "difficulty": "hard",
      "question": "Construct ΔABC with AB=6cm, BC=8cm, and median from A to BC=5cm. How many solutions? 🧩",
      "options": {
        "A": "0",
        "B": "1",
        "C": "2",
        "D": "3"
      },
      "correct_answer": "B"
    },
    {
      "id": 42,
      "difficulty": "hard",
      "question": "To construct a triangle given base, base angle, and sum of other two sides, we first draw: 🎨",
      "options": {
        "A": "the base",
        "B": "the base angle",
        "C": "a perpendicular",
        "D": "an arc"
      },
      "correct_answer": "A"
    },
    {
      "id": 43,
      "difficulty": "hard",
      "question": "Construct ΔXYZ with ∠Y=60°, ∠Z=45°, and XY+YZ+ZX=15cm. What is XY:YZ:ZX? 📊",
      "options": {
        "A": "2√2 : (√6+√2) : 2√3",
        "B": "2:3:4",
        "C": "3:4:5",
        "D": "1:√2:√3"
      },
      "correct_answer": "A"
    },
    {
      "id": 44,
      "difficulty": "hard",
      "question": "How many triangles can be constructed with angles 40°, 60°, 80° and perimeter 20cm? 🤯",
      "options": {
        "A": "0",
        "B": "1",
        "C": "2",
        "D": "Infinite"
      },
      "correct_answer": "B"
    },
    {
      "id": 45,
      "difficulty": "hard",
      "question": "Construct ΔABC with BC=7cm, ∠B=75°, and AB+AC=13cm. What is AB-AC? 🔍",
      "options": {
        "A": "1 cm",
        "B": "2 cm",
        "C": "3 cm",
        "D": "Cannot determine"
      },
      "correct_answer": "D"
    },
    {
      "id": 46,
      "difficulty": "hard",
      "question": "To construct a triangle given base, base angle, and difference of other two sides, the number of possible triangles is: ⚖️",
      "options": {
        "A": "0 or 1",
        "B": "1 or 2",
        "C": "0,1, or 2",
        "D": "Always 1"
      },
      "correct_answer": "C"
    },
    {
      "id": 47,
      "difficulty": "hard",
      "question": "Construct two triangles ABC and DEF with AB=DE=5cm, BC=EF=6cm, and median from A=median from D=4cm. Are they congruent? 🔺",
      "options": {
        "A": "Always",
        "B": "Never",
        "C": "Sometimes",
        "D": "Cannot construct"
      },
      "correct_answer": "C"
    },
    {
      "id": 48,
      "difficulty": "hard",
      "question": "Given circumradius R=5cm and two angles 45°, 60°, how many triangles possible? ⭕",
      "options": {
        "A": "0",
        "B": "1",
        "C": "2",
        "D": "Infinite"
      },
      "correct_answer": "B"
    },
    {
      "id": 49,
      "difficulty": "hard",
      "question": "Construct ΔPQR with PQ=8cm, PR=6cm, and ∠Q-∠R=30°. How many triangles? 📐",
      "options": {
        "A": "0",
        "B": "1",
        "C": "2",
        "D": "3"
      },
      "correct_answer": "A"
    },
    {
      "id": 50,
      "difficulty": "hard",
      "question": "To construct a triangle given its base, altitude, and vertical angle, we use: 🏔️",
      "options": {
        "A": "Arc of a circle",
        "B": "Perpendicular bisector",
        "C": "Angle bisector",
        "D": "Parallel lines"
      },
      "correct_answer": "A"
    },
    {
      "id": 51,
      "difficulty": "hard",
      "question": "Construct ΔABC with AB=5cm, AC=7cm, and angle between medians from B and C =90°. Is it unique? 🤔",
      "options": {
        "A": "Yes",
        "B": "No",
        "C": "Cannot construct",
        "D": "Depends on measurements"
      },
      "correct_answer": "A"
    },
    {
      "id": 52,
      "difficulty": "hard",
      "question": "How many triangles with integer sides have perimeter 15cm? 🔢",
      "options": { "A": "3", "B": "5", "C": "7", "D": "9" },
      "correct_answer": "C"
    },
    {
      "id": 53,
      "difficulty": "hard",
      "question": "Construct an isosceles triangle with base 10cm and circumradius 8cm. How many solutions? 🔄",
      "options": { "A": "0", "B": "1", "C": "2", "D": "4" },
      "correct_answer": "C"
    },
    {
      "id": 54,
      "difficulty": "hard",
      "question": "Given inradius r=3cm and two angles 50°, 70°, can we construct a unique triangle? ⚙️",
      "options": {
        "A": "Yes",
        "B": "No",
        "C": "Sometimes",
        "D": "With additional data"
      },
      "correct_answer": "A"
    },
    {
      "id": 55,
      "difficulty": "hard",
      "question": "Construct ΔABC with ∠A=60°, altitude from A=5cm, and BC=8cm. How many triangles? 📏",
      "options": { "A": "0", "B": "1", "C": "2", "D": "4" },
      "correct_answer": "C"
    },
    {
      "id": 56,
      "difficulty": "hard",
      "question": "To construct a triangle given its three medians, we first construct: 📍",
      "options": {
        "A": "a triangle with sides equal to medians",
        "B": "a parallelogram",
        "C": "another triangle with sides 2/3 of medians",
        "D": "a triangle with sides equal to 3/2 of medians"
      },
      "correct_answer": "A"
    },
    {
      "id": 57,
      "difficulty": "hard",
      "question": "Construct two different triangles with same SSS measurements. Are they congruent? 🔺",
      "options": {
        "A": "Yes",
        "B": "No",
        "C": "Sometimes",
        "D": "Cannot construct two different"
      },
      "correct_answer": "D"
    },
    {
      "id": 58,
      "difficulty": "hard",
      "question": "Given exradii ra=10cm, rb=12cm, rc=15cm, how many triangles possible? 🌀",
      "options": { "A": "0", "B": "1", "C": "2", "D": "Infinite" },
      "correct_answer": "B"
    },
    {
      "id": 59,
      "difficulty": "hard",
      "question": "Construct ΔABC with AB=6cm, AC=8cm, and angle bisector of A=5cm. How many triangles? ✂️",
      "options": {
        "A": "0",
        "B": "1",
        "C": "2",
        "D": "3"
      },
      "correct_answer": "B"
    },
    {
      "id": 60,
      "difficulty": "hard",
      "question": "Can we construct a triangle with sides equal to three given altitudes? 📐",
      "options": {
        "A": "Always",
        "B": "Never",
        "C": "Sometimes",
        "D": "Only for right triangles"
      },
      "correct_answer": "C"
    }
  ]
}