{
  "title": "Congruence of Triangles - Grade 7 ICSE",
  "total_questions": 60,
  "questions": [
    {
      "id": 1,
      "difficulty": "easy",
      "question": "Which symbol is used for congruence? 🔺",
      "options": { "A": "≈", "B": "≅", "C": "=", "D": "~" },
      "correct_answer": "B"
    },
    {
      "id": 2,
      "difficulty": "easy",
      "question": "If two triangles have the same size and shape, they are ______. 📐",
      "options": {
        "A": "similar",
        "B": "equal",
        "C": "congruent",
        "D": "equivalent"
      },
      "correct_answer": "C"
    },
    {
      "id": 3,
      "difficulty": "easy",
      "question": "How many criteria are there for triangle congruence? 🔢",
      "options": {
        "A": "3",
        "B": "4",
        "C": "5",
        "D": "6"
      },
      "correct_answer": "B"
    },
    {
      "id": 4,
      "difficulty": "easy",
      "question": "SSS stands for: 🧩",
      "options": {
        "A": "Side Side Side",
        "B": "Side Side Angle",
        "C": "Side Angle Side",
        "D": "Angle Side Side"
      },
      "correct_answer": "A"
    },
    {
      "id": 5,
      "difficulty": "easy",
      "question": "If two sides and the included angle of one triangle are equal to two sides and included angle of another, the triangles are congruent by ______ rule. ⚖️",
      "options": { "A": "ASA", "B": "SAS", "C": "SSS", "D": "RHS" },
      "correct_answer": "B"
    },
    {
      "id": 6,
      "difficulty": "easy",
      "question": "Which congruence criterion requires a right angle? ⬜",
      "options": { "A": "ASA", "B": "SAS", "C": "SSS", "D": "RHS" },
      "correct_answer": "D"
    },
    {
      "id": 7,
      "difficulty": "easy",
      "question": "If all three sides of one triangle are equal to three sides of another triangle, they are congruent by: 📏",
      "options": { "A": "AAA", "B": "SSS", "C": "SAS", "D": "ASA" },
      "correct_answer": "B"
    },
    {
      "id": 8,
      "difficulty": "easy",
      "question": "In ASA, 'A' stands for: 🧠",
      "options": { "A": "Angle", "B": "Area", "C": "Arc", "D": "Altitude" },
      "correct_answer": "A"
    },
    {
      "id": 9,
      "difficulty": "easy",
      "question": "If two angles and the included side of one triangle are equal to two angles and included side of another, it's ______ congruence. 🎯",
      "options": { "A": "SAS", "B": "ASA", "C": "AAS", "D": "SSS" },
      "correct_answer": "B"
    },
    {
      "id": 10,
      "difficulty": "easy",
      "question": "RHS congruence applies only to ______ triangles. 📐",
      "options": {
        "A": "acute",
        "B": "obtuse",
        "C": "right-angled",
        "D": "equilateral"
      },
      "correct_answer": "C"
    },
    {
      "id": 11,
      "difficulty": "easy",
      "question": "If ΔABC ≅ ΔDEF, then side AB corresponds to side: ↔️",
      "options": { "A": "DE", "B": "EF", "C": "FD", "D": "BC" },
      "correct_answer": "A"
    },
    {
      "id": 12,
      "difficulty": "easy",
      "question": "Two equilateral triangles with equal sides are always: 🔺🔺",
      "options": {
        "A": "similar",
        "B": "congruent",
        "C": "different",
        "D": "isosceles"
      },
      "correct_answer": "B"
    },
    {
      "id": 13,
      "difficulty": "easy",
      "question": "If ΔPQR ≅ ΔXYZ, then ∠P = ? ❓",
      "options": { "A": "∠X", "B": "∠Y", "C": "∠Z", "D": "∠Q" },
      "correct_answer": "A"
    },
    {
      "id": 14,
      "difficulty": "easy",
      "question": "AAA (Angle-Angle-Angle) ensures triangles are ______ but not necessarily congruent. 👯",
      "options": {
        "A": "equal",
        "B": "similar",
        "C": "identical",
        "D": "different"
      },
      "correct_answer": "B"
    },
    {
      "id": 15,
      "difficulty": "easy",
      "question": "Which is NOT a congruence criterion? 🚫",
      "options": { "A": "SSS", "B": "SAS", "C": "AAA", "D": "RHS" },
      "correct_answer": "C"
    },
    {
      "id": 16,
      "difficulty": "easy",
      "question": "If two triangles are congruent, their perimeters are: 📊",
      "options": { "A": "different", "B": "equal", "C": "double", "D": "half" },
      "correct_answer": "B"
    },
    {
      "id": 17,
      "difficulty": "easy",
      "question": "In RHS, 'H' stands for: 🏔️",
      "options": {
        "A": "Height",
        "B": "Hypotenuse",
        "C": "Horizontal",
        "D": "Half"
      },
      "correct_answer": "B"
    },
    {
      "id": 18,
      "difficulty": "easy",
      "question": "If ΔABC ≅ ΔDEF, then BC = ? 📍",
      "options": { "A": "DE", "B": "EF", "C": "FD", "D": "CA" },
      "correct_answer": "B"
    },
    {
      "id": 19,
      "difficulty": "easy",
      "question": "Two triangles with equal corresponding angles and equal corresponding sides are: ✅",
      "options": {
        "A": "similar only",
        "B": "congruent",
        "C": "different",
        "D": "parallel"
      },
      "correct_answer": "B"
    },
    {
      "id": 20,
      "difficulty": "easy",
      "question": "For SAS congruence, the angle must be ______ the two sides. 🔄",
      "options": {
        "A": "opposite to",
        "B": "adjacent to",
        "C": "included between",
        "D": "far from"
      },
      "correct_answer": "C"
    },
    {
      "id": 21,
      "difficulty": "medium",
      "question": "In ΔABC and ΔDEF, if AB=DE, BC=EF, and ∠B=∠E, by which rule are they congruent? 🧭",
      "options": { "A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS" },
      "correct_answer": "B"
    },
    {
      "id": 22,
      "difficulty": "medium",
      "question": "If two right triangles have their hypotenuses equal and one pair of legs equal, they are congruent by: 🔺",
      "options": { "A": "SAS", "B": "ASA", "C": "RHS", "D": "SSS" },
      "correct_answer": "C"
    },
    {
      "id": 23,
      "difficulty": "medium",
      "question": "In ΔPQR and ΔXYZ, PQ=XY, QR=YZ, PR=XZ. They are congruent by: 🔗",
      "options": { "A": "SAS", "B": "ASA", "C": "SSS", "D": "RHS" },
      "correct_answer": "C"
    },
    {
      "id": 24,
      "difficulty": "medium",
      "question": "If ΔABC ≅ ΔPQR and AB=5 cm, what is the length of PQ? 📏",
      "options": { "A": "3 cm", "B": "5 cm", "C": "7 cm", "D": "10 cm" },
      "correct_answer": "B"
    },
    {
      "id": 25,
      "difficulty": "medium",
      "question": "Which additional information will make ΔABC ≅ ΔDEF by ASA? Given: ∠B=∠E and BC=EF. 🎲",
      "options": { "A": "AB=DE", "B": "∠A=∠D", "C": "∠C=∠F", "D": "AC=DF" },
      "correct_answer": "C"
    },
    {
      "id": 26,
      "difficulty": "medium",
      "question": "Two triangles are congruent if two angles and the non-included side of one are equal to two angles and the corresponding non-included side of the other. This is: 📝",
      "options": { "A": "ASA", "B": "AAS", "C": "SAS", "D": "SSA" },
      "correct_answer": "B"
    },
    {
      "id": 27,
      "difficulty": "medium",
      "question": "In congruent triangles, corresponding ______ are equal. 📐",
      "options": {
        "A": "areas",
        "B": "medians",
        "C": "altitudes",
        "D": "all of these"
      },
      "correct_answer": "D"
    },
    {
      "id": 28,
      "difficulty": "medium",
      "question": "If ΔABC ≅ ΔDEF and ∠A=60°, ∠B=70°, what is ∠F? ❓",
      "options": { "A": "50°", "B": "60°", "C": "70°", "D": "80°" },
      "correct_answer": "A"
    },
    {
      "id": 29,
      "difficulty": "medium",
      "question": "Which condition does NOT guarantee congruence? ⚠️",
      "options": { "A": "SSS", "B": "SAS", "C": "SSA", "D": "ASA" },
      "correct_answer": "C"
    },
    {
      "id": 30,
      "difficulty": "medium",
      "question": "If two isosceles triangles have equal bases and equal base angles, they are congruent by: 🏗️",
      "options": { "A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS" },
      "correct_answer": "C"
    },
    {
      "id": 31,
      "difficulty": "medium",
      "question": "ΔABC and ΔPQR are right-angled at B and Q. If AC=PR and AB=PQ, they are congruent by: ⚡",
      "options": { "A": "RHS", "B": "SAS", "C": "ASA", "D": "SSS" },
      "correct_answer": "A"
    },
    {
      "id": 32,
      "difficulty": "medium",
      "question": "If three angles of one triangle are equal to three angles of another, the triangles are: 👥",
      "options": {
        "A": "congruent",
        "B": "similar",
        "C": "equal",
        "D": "isosceles"
      },
      "correct_answer": "B"
    },
    {
      "id": 33,
      "difficulty": "medium",
      "question": "In ΔABC ≅ ΔXYZ, if AB=6cm, BC=8cm, CA=10cm, what is YZ? 🧮",
      "options": { "A": "6 cm", "B": "8 cm", "C": "10 cm", "D": "12 cm" },
      "correct_answer": "B"
    },
    {
      "id": 34,
      "difficulty": "medium",
      "question": "For ASA congruence, 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": 35,
      "difficulty": "medium",
      "question": "If two triangles have equal areas, are they always congruent? 🤔",
      "options": {
        "A": "Yes",
        "B": "No",
        "C": "Sometimes",
        "D": "Always for right triangles"
      },
      "correct_answer": "B"
    },
    {
      "id": 36,
      "difficulty": "medium",
      "question": "Which pair of triangles is definitely congruent? ✅",
      "options": {
        "A": "Two equilateral triangles with side 5 cm each",
        "B": "Two right triangles with hypotenuse 10 cm each",
        "C": "Two triangles with angles 30°, 60°, 90° each",
        "D": "Two isosceles triangles with base 6 cm each"
      },
      "correct_answer": "A"
    },
    {
      "id": 37,
      "difficulty": "medium",
      "question": "If ΔABC ≅ ΔDEF, and perimeter of ΔABC is 24 cm, perimeter of ΔDEF is: 📏",
      "options": { "A": "12 cm", "B": "24 cm", "C": "36 cm", "D": "48 cm" },
      "correct_answer": "B"
    },
    {
      "id": 38,
      "difficulty": "medium",
      "question": "In RHS congruence, besides right angle and hypotenuse, we need: 🔍",
      "options": {
        "A": "one more angle",
        "B": "one more side",
        "C": "included angle",
        "D": "any leg"
      },
      "correct_answer": "B"
    },
    {
      "id": 39,
      "difficulty": "medium",
      "question": "Two triangles with sides 3,4,5 cm and 4,5,3 cm are: 🔄",
      "options": {
        "A": "congruent",
        "B": "similar",
        "C": "different",
        "D": "right triangles"
      },
      "correct_answer": "A"
    },
    {
      "id": 40,
      "difficulty": "medium",
      "question": "If ΔPQR ≅ ΔLMN, and QR = 12 cm, what is MN? 📍",
      "options": { "A": "6 cm", "B": "12 cm", "C": "18 cm", "D": "24 cm" },
      "correct_answer": "B"
    },
    {
      "id": 41,
      "difficulty": "hard",
      "question": "In quadrilateral ABCD, diagonal AC divides it into two triangles. If AB=CD and BC=AD, are ΔABC and ΔCDA congruent? If yes, by which rule? 🧩",
      "options": {
        "A": "Yes, by SSS",
        "B": "Yes, by SAS",
        "C": "No",
        "D": "Yes, by RHS"
      },
      "correct_answer": "A"
    },
    {
      "id": 42,
      "difficulty": "hard",
      "question": "In ΔABC and ΔDEF, AB=DE, ∠A=∠D, and ∠B=∠E. What additional condition will make them congruent by ASA? 🎯",
      "options": {
        "A": "BC=EF",
        "B": "AC=DF",
        "C": "∠C=∠F",
        "D": "No additional condition needed"
      },
      "correct_answer": "D"
    },
    {
      "id": 43,
      "difficulty": "hard",
      "question": "If two triangles have two pairs of equal sides and the angles opposite to one pair of equal sides are equal, are they congruent? 🤯",
      "options": {
        "A": "Always",
        "B": "Never",
        "C": "Sometimes",
        "D": "Only for right triangles"
      },
      "correct_answer": "C"
    },
    {
      "id": 44,
      "difficulty": "hard",
      "question": "In ΔABC, AB=AC. D is midpoint of BC. Prove ΔABD ≅ ΔACD. Which congruence rule applies? 🔺",
      "options": { "A": "SSS", "B": "SAS", "C": "RHS", "D": "ASA" },
      "correct_answer": "A"
    },
    {
      "id": 45,
      "difficulty": "hard",
      "question": "Two right triangles have equal hypotenuses. What additional condition guarantees congruence? ⚡",
      "options": {
        "A": "One acute angle equal",
        "B": "One leg equal",
        "C": "Both acute angles equal",
        "D": "Any one side equal"
      },
      "correct_answer": "B"
    },
    {
      "id": 46,
      "difficulty": "hard",
      "question": "In ΔPQR and ΔXYZ, PQ=XY, ∠P=∠X, and PR=XZ. Are they necessarily congruent? 💭",
      "options": {
        "A": "Yes, by SAS",
        "B": "Yes, by ASA",
        "C": "No, SSA is not valid",
        "D": "Yes, by RHS"
      },
      "correct_answer": "C"
    },
    {
      "id": 47,
      "difficulty": "hard",
      "question": "If three medians of one triangle are equal to three medians of another, are the triangles congruent? 📐",
      "options": {
        "A": "Yes",
        "B": "No",
        "C": "Sometimes",
        "D": "Only if equilateral"
      },
      "correct_answer": "B"
    },
    {
      "id": 48,
      "difficulty": "hard",
      "question": "In an isosceles triangle ABC with AB=AC, the altitude AD from A to BC proves ΔABD ≅ ΔACD by: 🏔️",
      "options": { "A": "SSS", "B": "SAS", "C": "RHS", "D": "ASA" },
      "correct_answer": "C"
    },
    {
      "id": 49,
      "difficulty": "hard",
      "question": "Two triangles have equal perimeters and equal areas. Are they congruent? 📊",
      "options": {
        "A": "Always",
        "B": "Never",
        "C": "Sometimes",
        "D": "Only if right-angled"
      },
      "correct_answer": "C"
    },
    {
      "id": 50,
      "difficulty": "hard",
      "question": "In ΔABC, D and E are points on AB and AC such that AD=AE and ∠ADC=∠AEB. Prove ΔADC ≅ ΔAEB. Which rule? 🔍",
      "options": { "A": "ASA", "B": "SAS", "C": "AAS", "D": "SSS" },
      "correct_answer": "C"
    },
    {
      "id": 51,
      "difficulty": "hard",
      "question": "If two triangles are congruent, their circumcircles have: ⭕",
      "options": {
        "A": "equal radii",
        "B": "different radii",
        "C": "same center",
        "D": "no relation"
      },
      "correct_answer": "A"
    },
    {
      "id": 52,
      "difficulty": "hard",
      "question": "In a parallelogram ABCD, diagonal AC creates two triangles. Are ΔABC and ΔCDA congruent? If yes, by which rule? ▱",
      "options": {
        "A": "Yes, by SSS",
        "B": "Yes, by SAS",
        "C": "Yes, by ASA",
        "D": "No"
      },
      "correct_answer": "B"
    },
    {
      "id": 53,
      "difficulty": "hard",
      "question": "Two triangles have sides 5,12,13 and 12,13,5. They are: 🔄",
      "options": {
        "A": "congruent",
        "B": "similar but not congruent",
        "C": "different",
        "D": "right triangles only"
      },
      "correct_answer": "A"
    },
    {
      "id": 54,
      "difficulty": "hard",
      "question": "If ΔABC ≅ ΔPQR under the correspondence ABC↔QRP, then ∠A corresponds to: 🔀",
      "options": { "A": "∠P", "B": "∠Q", "C": "∠R", "D": "∠B" },
      "correct_answer": "B"
    },
    {
      "id": 55,
      "difficulty": "hard",
      "question": "In an equilateral triangle, all three altitudes are equal. If two equilateral triangles have equal altitudes, are they congruent? ⚖️",
      "options": {
        "A": "Yes",
        "B": "No",
        "C": "Sometimes",
        "D": "Only if sides are equal"
      },
      "correct_answer": "A"
    },
    {
      "id": 56,
      "difficulty": "hard",
      "question": "Which of these conditions ensures congruence in right triangles? 🎲",
      "options": {
        "A": "Hypotenuse and one acute angle equal",
        "B": "Two acute angles equal",
        "C": "One leg and one acute angle equal",
        "D": "Both A and C"
      },
      "correct_answer": "D"
    },
    {
      "id": 57,
      "difficulty": "hard",
      "question": "If two triangles have five pairs of equal elements (sides and angles), they must be: ✅",
      "options": {
        "A": "congruent",
        "B": "similar",
        "C": "isosceles",
        "D": "equilateral"
      },
      "correct_answer": "A"
    },
    {
      "id": 58,
      "difficulty": "hard",
      "question": "In ΔABC and ΔDEF, AB=DE, BC=EF, and median from A to BC = median from D to EF. Are they congruent? 🤔",
      "options": {
        "A": "Yes, by SSS",
        "B": "Yes, by SAS",
        "C": "No",
        "D": "Yes, by RHS"
      },
      "correct_answer": "C"
    },
    {
      "id": 59,
      "difficulty": "hard",
      "question": "Two congruent triangles are always similar with similarity ratio: 🔢",
      "options": { "A": "1:1", "B": "1:2", "C": "2:1", "D": "varies" },
      "correct_answer": "A"
    },
    {
      "id": 60,
      "difficulty": "hard",
      "question": "If ΔABC ≅ ΔDEF and the area of ΔABC is 36 cm², what is the area of ΔDEF? 📐",
      "options": {
        "A": "18 cm²",
        "B": "36 cm²",
        "C": "72 cm²",
        "D": "144 cm²"
      },
      "correct_answer": "B"
    }
  ]
}