{
  "title": "Meaning of Congruence - Grade 7 CBSE",
  "total_questions": 150,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "What does congruence mean in geometry?", "options": {"A": "Same shape", "B": "Same size", "C": "Same shape and size", "D": "Similar appearance"}, "correct_answer": "C"},
    {"id": 2, "difficulty": "easy", "question": "If two figures are congruent, they can be made to coincide by:", "options": {"A": "Rotation", "B": "Reflection", "C": "Translation", "D": "All of these"}, "correct_answer": "D"},
    {"id": 3, "difficulty": "easy", "question": "The symbol for congruence is:", "options": {"A": "=", "B": "≈", "C": "≅", "D": "∼"}, "correct_answer": "C"},
    {"id": 4, "difficulty": "easy", "question": "Two figures that are identical in shape and size are:", "options": {"A": "Similar", "B": "Congruent", "C": "Equivalent", "D": "Parallel"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "If ΔABC ≅ ΔPQR, then:", "options": {"A": "AB = PQ", "B": "∠A = ∠P", "C": "Both A and B", "D": "Neither A nor B"}, "correct_answer": "C"},
    {"id": 6, "difficulty": "easy", "question": "Congruent figures have:", "options": {"A": "Equal areas", "B": "Equal perimeters", "C": "Both A and B", "D": "Different areas"}, "correct_answer": "C"},
    {"id": 7, "difficulty": "easy", "question": "If two circles have equal radii, they are:", "options": {"A": "Similar", "B": "Congruent", "C": "Concentric", "D": "Tangent"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "Which is true about congruent triangles?", "options": {"A": "Corresponding sides equal", "B": "Corresponding angles equal", "C": "Both A and B", "D": "Only angles equal"}, "correct_answer": "C"},
    {"id": 9, "difficulty": "easy", "question": "If two squares have equal sides, they are:", "options": {"A": "Similar", "B": "Congruent", "C": "Both", "D": "Neither"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "Congruence is a relation between:", "options": {"A": "Points", "B": "Figures", "C": "Numbers", "D": "Equations"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "If two line segments have equal length, they are:", "options": {"A": "Parallel", "B": "Congruent", "C": "Perpendicular", "D": "Collinear"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "Two figures that are congruent must have:", "options": {"A": "Same position", "B": "Same orientation", "C": "Same measurements", "D": "Same color"}, "correct_answer": "C"},
    {"id": 13, "difficulty": "easy", "question": "If ∠A ≅ ∠B, then:", "options": {"A": "∠A = ∠B", "B": "∠A + ∠B = 90°", "C": "∠A + ∠B = 180°", "D": "∠A is adjacent to ∠B"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "Congruent figures can be:", "options": {"A": "Rotated versions", "B": "Mirror images", "C": "Shifted positions", "D": "All of these"}, "correct_answer": "D"},
    {"id": 15, "difficulty": "easy", "question": "If two rectangles have same length and width, they are:", "options": {"A": "Similar", "B": "Congruent", "C": "Different", "D": "Parallel"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "The word 'congruent' comes from Latin meaning:", "options": {"A": "Same shape", "B": "Agreeing", "C": "Equal", "D": "Parallel"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "If two triangles are congruent, their areas are:", "options": {"A": "Equal", "B": "Different", "C": "Proportional", "D": "Cannot say"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "Which statement is always true for congruent figures?", "options": {"A": "They are similar", "B": "They have same shape and size", "C": "They are in same position", "D": "They are equilateral"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "If two angles are congruent, they have:", "options": {"A": "Same measure", "B": "Same vertex", "C": "Same arms", "D": "Same position"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "Congruence preserves:", "options": {"A": "Size", "B": "Shape", "C": "Both size and shape", "D": "Position"}, "correct_answer": "C"},
    
    {"id": 21, "difficulty": "medium", "question": "If ΔABC ≅ ΔDEF, which correspondence is correct?", "options": {"A": "A↔D, B↔E, C↔F", "B": "A↔E, B↔F, C↔D", "C": "A↔F, B↔D, C↔E", "D": "Any of these"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "Two figures are congruent if one can be obtained from the other by:", "options": {"A": "Rotation only", "B": "Reflection only", "C": "Translation only", "D": "Any rigid motion"}, "correct_answer": "D"},
    {"id": 23, "difficulty": "medium", "question": "If quadrilateral ABCD ≅ quadrilateral PQRS, then AB corresponds to:", "options": {"A": "PQ", "B": "QR", "C": "RS", "D": "SP"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "Which transformation does NOT preserve congruence?", "options": {"A": "Rotation", "B": "Reflection", "C": "Dilation", "D": "Translation"}, "correct_answer": "C"},
    {"id": 25, "difficulty": "medium", "question": "If two triangles have equal areas, are they necessarily congruent?", "options": {"A": "Always", "B": "Sometimes", "C": "Never", "D": "Cannot determine"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "In congruence, the order of vertices matters because:", "options": {"A": "It shows correspondence", "B": "It affects area", "C": "It changes shape", "D": "It doesn't matter"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "If two polygons are congruent, they have same number of:", "options": {"A": "Sides", "B": "Vertices", "C": "Both A and B", "D": "Diagonals"}, "correct_answer": "C"},
    {"id": 28, "difficulty": "medium", "question": "Which is sufficient to prove two triangles congruent?", "options": {"A": "All angles equal", "B": "Two sides equal", "C": "Two angles and included side equal", "D": "Perimeter equal"}, "correct_answer": "C"},
    {"id": 29, "difficulty": "medium", "question": "If ΔABC ≅ ΔPQR, then area of ΔABC : area of ΔPQR =", "options": {"A": "1:1", "B": "1:2", "C": "2:1", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "Congruence is an equivalence relation because it is:", "options": {"A": "Reflexive", "B": "Symmetric", "C": "Transitive", "D": "All of these"}, "correct_answer": "D"},
    {"id": 31, "difficulty": "medium", "question": "If two figures are mirror images, they are:", "options": {"A": "Always congruent", "B": "Sometimes congruent", "C": "Never congruent", "D": "Similar only"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "Which property is preserved in congruence?", "options": {"A": "Distance between points", "B": "Angle measures", "C": "Both A and B", "D": "Neither A nor B"}, "correct_answer": "C"},
    {"id": 33, "difficulty": "medium", "question": "If two circles are congruent, they have same:", "options": {"A": "Radius", "B": "Diameter", "C": "Circumference", "D": "All of these"}, "correct_answer": "D"},
    {"id": 34, "difficulty": "medium", "question": "Two figures can be congruent even if they are:", "options": {"A": "Different colors", "B": "Different materials", "C": "Different positions", "D": "All of these"}, "correct_answer": "D"},
    {
    "id": 35,
    "difficulty": "medium",
    "question": "If AB ≅ CD, and AB = 3x+7, CD = 5x-13, find length.",
    "options": {
      "A": "22 cm",
      "B": "28 cm",
      "C": "34 cm",
      "D": "37 cm"
    },
    "correct_answer": "D"
  }, {"id": 36, "difficulty": "medium", "question": "Which statement about congruence is false?", "options": {"A": "Congruent figures have equal areas", "B": "Congruent figures are always similar", "C": "Congruent figures can be in different positions", "D": "All similar figures are congruent"}, "correct_answer": "D"},
    {"id": 37, "difficulty": "medium", "question": "If two line segments are congruent, their midpoints divide them into segments that are:", "options": {"A": "Congruent", "B": "Similar", "C": "Proportional", "D": "Equal in number"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "In real life, congruence is important in:", "options": {"A": "Manufacturing", "B": "Architecture", "C": "Art", "D": "All of these"}, "correct_answer": "D"},
    {"id": 39, "difficulty": "medium", "question": "If two angles are congruent, their supplements are:", "options": {"A": "Equal", "B": "Complementary", "C": "Supplementary", "D": "Different"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "Which figures are always congruent to themselves?", "options": {"A": "All figures", "B": "Only regular polygons", "C": "Only triangles", "D": "Only circles"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "medium", "question": "If two triangles have all sides equal, they are congruent by:", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "medium", "question": "Congruence preserves collinearity, meaning:", "options": {"A": "Points on line remain on line", "B": "Lines remain parallel", "C": "Angles remain equal", "D": "All of these"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "If two squares have equal areas, they are:", "options": {"A": "Similar", "B": "Congruent", "C": "Both", "D": "Neither"}, "correct_answer": "B"},
    {
    "id": 44,
    "difficulty": "medium",
    "question": "If PQ = (7x-11) cm, RS = (5x+13) cm are congruent, find length.",
    "options": {
      "A": "38 cm",
      "B": "45 cm",
      "C": "52 cm",
      "D": "73 cm"
    },
    "correct_answer": "D"
  },  {"id": 45, "difficulty": "medium", "question": "If ΔABC ≅ ΔPQR and ΔPQR ≅ ΔXYZ, then:", "options": {"A": "ΔABC ≅ ΔXYZ", "B": "ΔABC is similar to ΔXYZ", "C": "ΔABC = ΔXYZ", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "medium", "question": "Two congruent figures placed on each other will:", "options": {"A": "Coincide exactly", "B": "Overlap partially", "C": "Not overlap", "D": "Have gaps"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "medium", "question": "If two triangles have equal perimeters, are they congruent?", "options": {"A": "Always", "B": "Sometimes", "C": "Never", "D": "Cannot say"}, "correct_answer": "B"},
    {"id": 48, "difficulty": "medium", "question": "Congruence is to size as similarity is to:", "options": {"A": "Shape", "B": "Scale", "C": "Both", "D": "Neither"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "medium", "question": "If two circles are congruent, any chord of one circle is equal to:", "options": {"A": "Corresponding chord of other", "B": "Diameter of other", "C": "Radius of other", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "medium", "question": "Which transformation preserves both congruence and orientation?", "options": {"A": "Translation", "B": "Reflection", "C": "Rotation of 180°", "D": "All of these"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "medium", "question": "If two quadrilaterals are congruent, their diagonals are:", "options": {"A": "Equal", "B": "Proportional", "C": "Perpendicular", "D": "Parallel"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "medium", "question": "Congruent figures have same:", "options": {"A": "Shape", "B": "Size", "C": "Both", "D": "Neither"}, "correct_answer": "C"},
    {"id": 53, "difficulty": "medium", "question": "If two triangles are congruent by SAS, how many pairs of equal parts are guaranteed?", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "medium", "question": "Which is true? Every congruent figure is:", "options": {"A": "Similar", "B": "Equal", "C": "Identical", "D": "All of these"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "medium", "question": "If two line segments are congruent, any point dividing one in ratio m:n will divide other:", "options": {"A": "In same ratio", "B": "In different ratio", "C": "Equally", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "medium", "question": "Two congruent triangles will always have same:", "options": {"A": "Area", "B": "Perimeter", "C": "Both", "D": "Neither"}, "correct_answer": "C"},
    {"id": 57, "difficulty": "medium", "question": "If ΔABC ≅ ΔDEF, then median from A corresponds to:", "options": {"A": "Median from D", "B": "Median from E", "C": "Median from F", "D": "Altitude from D"}, "correct_answer": "A"},
     {
    "id": 58,
    "difficulty": "medium",
    "question": "If PQ ≅ QR ≅ RS, and PQ = 4x-3, RS = 3x+6, find length.",
    "options": {
      "A": "15 cm",
      "B": "18 cm",
      "C": "21 cm",
      "D": "33 cm"
    },
    "correct_answer": "D"
  }, {"id": 59, "difficulty": "medium", "question": "If two angles are congruent and complementary, each is:", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "B"},
    {"id": 60, "difficulty": "medium", "question": "Which congruence criterion requires right angle?", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS"}, "correct_answer": "D"},
    {"id": 61, "difficulty": "medium", "question": "If two polygons are congruent, their corresponding sides are:", "options": {"A": "Equal", "B": "Parallel", "C": "Perpendicular", "D": "Collinear"}, "correct_answer": "A"},
    {"id": 62, "difficulty": "medium", "question": "Congruent figures can be thought of as:", "options": {"A": "Carbon copies", "B": "Photocopies", "C": "Clones", "D": "All of these"}, "correct_answer": "D"},
    {"id": 63, "difficulty": "medium", "question": "If two triangles have two angles equal, they are:", "options": {"A": "Congruent", "B": "Similar", "C": "Both", "D": "Neither"}, "correct_answer": "B"},
    {"id": 64, "difficulty": "medium", "question": "Which is reflexive property of congruence?", "options": {"A": "If a ≅ b then b ≅ a", "B": "If a ≅ b and b ≅ c then a ≅ c", "C": "a ≅ a", "D": "All of these"}, "correct_answer": "C"},
    {"id": 65, "difficulty": "medium", "question": "If two circles are congruent, arcs subtending equal angles are:", "options": {"A": "Equal", "B": "Proportional", "C": "Complementary", "D": "Supplementary"}, "correct_answer": "A"},
    {"id": 66, "difficulty": "medium", "question": "Congruence implies:", "options": {"A": "Equality of all parts", "B": "Correspondence of parts", "C": "Similarity", "D": "All of these"}, "correct_answer": "D"},
    {"id": 67, "difficulty": "medium", "question": "If two triangles are congruent, their altitudes are:", "options": {"A": "Equal", "B": "Proportional", "C": "Parallel", "D": "Perpendicular"}, "correct_answer": "A"},
    {"id": 68, "difficulty": "medium", "question": "Which transformation changes congruence to similarity?", "options": {"A": "Translation", "B": "Rotation", "C": "Dilation", "D": "Reflection"}, "correct_answer": "C"},
    {"id": 69, "difficulty": "medium", "question": "If two line segments are congruent, they have same:", "options": {"A": "Length", "B": "Slope", "C": "Position", "D": "All of these"}, "correct_answer": "A"},
    {"id": 70, "difficulty": "medium", "question": "Congruent triangles have same:", "options": {"A": "Shape", "B": "Size", "C": "Both", "D": "Neither"}, "correct_answer": "C"},
    {"id": 71, "difficulty": "medium", "question": "If ΔABC ≅ ΔPQR, then angle bisector of ∠A corresponds to:", "options": {"A": "Angle bisector of ∠P", "B": "Angle bisector of ∠Q", "C": "Angle bisector of ∠R", "D": "Median from P"}, "correct_answer": "A"},
    {"id": 72, "difficulty": "medium", "question": "Which is symmetric property of congruence?", "options": {"A": "If a ≅ b then b ≅ a", "B": "a ≅ a", "C": "If a ≅ b and b ≅ c then a ≅ c", "D": "All of these"}, "correct_answer": "A"},
    {"id": 73, "difficulty": "medium", "question": "If two squares are congruent, their diagonals are:", "options": {"A": "Equal", "B": "Perpendicular", "C": "Both", "D": "Neither"}, "correct_answer": "C"},
    {"id": 74, "difficulty": "medium", "question": "Congruence is used to prove:", "options": {"A": "Equality of segments", "B": "Equality of angles", "C": "Parallelism", "D": "All of these"}, "correct_answer": "D"},
    {"id": 75, "difficulty": "medium", "question": "If two triangles are congruent, their circumcircles have:", "options": {"A": "Equal radii", "B": "Different radii", "C": "Same center", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 76, "difficulty": "medium", "question": "Which is transitive property of congruence?", "options": {"A": "If a ≅ b then b ≅ a", "B": "a ≅ a", "C": "If a ≅ b and b ≅ c then a ≅ c", "D": "All of these"}, "correct_answer": "C"},
    {"id": 77, "difficulty": "medium", "question": "If two rectangles are congruent, they have same:", "options": {"A": "Length and width", "B": "Area", "C": "Perimeter", "D": "All of these"}, "correct_answer": "D"},
    {"id": 78, "difficulty": "medium", "question": "Congruent arcs in congruent circles subtend:", "options": {"A": "Equal angles", "B": "Complementary angles", "C": "Supplementary angles", "D": "Right angles"}, "correct_answer": "A"},
    {"id": 79, "difficulty": "medium", "question": "If two triangles are congruent, their incircles have:", "options": {"A": "Equal radii", "B": "Different radii", "C": "Same center", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "medium", "question": "Congruence preserves:", "options": {"A": "Distance", "B": "Angle", "C": "Area", "D": "All of these"}, "correct_answer": "D"},
    
     {
    "id": 81,
    "difficulty": "hard",
    "question": "In quadrilateral ABCD ≅ quadrilateral PQRS, AB = (3x+2) cm, PQ = 20 cm, BC = (2y-3) cm, QR = 17 cm, CD = (4z-5) cm, RS = 23 cm. Find x+y+z.",
    "options": {
      "A": "20",
      "B": "23",
      "C": "26",
      "D": "29"
    },
    "correct_answer": "B"
  },  {"id": 82, "difficulty": "hard", "question": "Two congruent regular polygons have each interior angle 156°. How many sides do they have?", "options": {"A": "12", "B": "15", "C": "18", "D": "20"}, "correct_answer": "B"},
     {
    "id": 83,
    "difficulty": "hard",
    "question": "In ΔABC ≅ ΔPQR, AB = (2a+3) cm, PQ = 15 cm, BC = (3b-4) cm, QR = 20 cm, CA = (4c-5) cm, RP = 25 cm. Find a+b+c.",
    "options": {
      "A": "15",
      "B": "18",
      "C": "21",
      "D": "24"
    },
    "correct_answer": "C"
  },  {
  "id": 84,
  "difficulty": "hard",
  "question": "Two congruent circles each have radius 10 cm. If the distance between their centres is 12 cm, what is the length of the common chord?",
  "options": {
    "A": "12 cm",
    "B": "14 cm",
    "C": "16 cm",
    "D": "18 cm"
  },
  "correct_answer": "C"
}
, {"id": 85, "difficulty": "hard", "question": "In ΔABC ≅ ΔDEF, if ∠A = (3x+10)°, ∠D = 70°, ∠B = (4y-20)°, ∠E = 60°, find x and y.", "options": {"A": "x=20, y=20", "B": "x=25, y=15", "C": "x=30, y=10", "D": "x=35, y=5"}, "correct_answer": "A"},
     {
    "id": 86,
    "difficulty": "hard",
    "question": "Two congruent isosceles triangles have perimeter 50 cm. Equal sides are 5 cm more than base. Find area if height to base is 12 cm.",
    "options": {
      "A": "60 cm²",
      "B": "84 cm²",
      "C": "96 cm²",
      "D": "80 cm²"
    },
    "correct_answer": "D"
  },  {
  "id": 87,
  "difficulty": "hard",
  "question": "Two congruent regular hexagons have distance between parallel opposite sides equal to 10√3 cm. What is the area of each hexagon?",
  "options": {
    "A": "150√3 cm²",
    "B": "200√3 cm²",
    "C": "250√3 cm²",
    "D": "300√3 cm²"
  },
  "correct_answer": "A"
}
,   {
    "id": 88,
    "difficulty": "hard",
    "question": "In parallelogram ABCD ≅ parallelogram PQRS, AB = (3x-2) cm, PQ = 16 cm, BC = (4y+1) cm, QR = 25 cm, ∠A = (5z+10)°, ∠P = 60°. Find x+y+z.",
    "options": {
      "A": "15",
      "B": "18",
      "C": "22",
      "D": "24"
    },
    "correct_answer": "C"
  },  {"id": 89, "difficulty": "hard", "question": "Two congruent sectors of circle have radius 21 cm and central angle 120°. Find area of each sector (π=22/7).", "options": {"A": "154 cm²", "B": "308 cm²", "C": "462 cm²", "D": "616 cm²"}, "correct_answer": "C"},
    {"id": 90, "difficulty": "hard", "question": "In rhombus ABCD ≅ rhombus PQRS, diagonal AC = 24 cm, BD = 10 cm. Find side length and area of each rhombus.", "options": {"A": "Side=13 cm, Area=120 cm²", "B": "Side=13 cm, Area=130 cm²", "C": "Side=15 cm, Area=120 cm²", "D": "Side=15 cm, Area=150 cm²"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "Two congruent cylinders have total surface area 2992 cm² (π=22/7). If height is 20 cm, find radius.", "options": {"A": "7 cm", "B": "14 cm", "C": "21 cm", "D": "28 cm"}, "correct_answer": "B"},
    {
    "id": 92,
    "difficulty": "hard",
    "question": "In ΔABC ≅ ΔPQR, if AB = (2a+3) cm, PQ = 15 cm, ∠A = (3b+10)°, ∠P = 55°, BC = (4c-5) cm, QR = 23 cm, find a+b+c.",
    "options": {
      "A": "15",
      "B": "18",
      "C": "21",
      "D": "28"
    },
    "correct_answer": "D"
  }, {"id": 93, "difficulty": "hard", "question": "Two congruent cones have slant height 25 cm and radius 7 cm. Find volume of each cone (π=22/7).", "options": {"A": "616 cm³", "B": "1232 cm³", "C": "1848 cm³", "D": "2464 cm³"}, "correct_answer": "B"},
    {"id": 94, "difficulty": "hard", "question": "In trapezium ABCD ≅ trapezium PQRS with AB∥CD, PQ∥RS. AB = 15 cm, CD = 25 cm, AD = BC = 13 cm. Find height and area.", "options": {"A": "h=12 cm, A=240 cm²", "B": "h=12 cm, A=260 cm²", "C": "h=13 cm, A=240 cm²", "D": "h=13 cm, A=260 cm²"}, "correct_answer": "A"},
    {"id": 95, "difficulty": "hard", "question": "Two congruent spheres have surface area 616 cm² (π=22/7). Find volume.", "options": {"A": "1437.33 cm³", "B": "1796.67 cm³", "C": "2156 cm³", "D": "2515.33 cm³"}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "In regular pentagon ABCDE ≅ regular pentagon PQRST, each side = 10 cm. Find area of each pentagon if apothem = 6.88 cm.", "options": {"A": "137.6 cm²", "B": "172 cm²", "C": "206.4 cm²", "D": "240.8 cm²"}, "correct_answer": "B"},
     {
    "id": 97,
    "difficulty": "hard",
    "question": "Two congruent pyramids have square base side 14 cm and slant height 25 cm. Find total surface area.",
    "options": {
      "A": "896 cm²",
      "B": "1008 cm²",
      "C": "1120 cm²",
      "D": "1232 cm²"
    },
    "correct_answer": "A"
  },   {
    "id": 98,
    "difficulty": "hard",
    "question": "In ΔXYZ ≅ ΔLMN, XY = (3p+2) cm, LM = 23 cm, ∠X = (4q-5)°, ∠L = 75°, YZ = (5r-3) cm, MN = 37 cm. Find p+q+r.",
    "options": {
      "A": "20",
      "B": "23",
      "C": "26",
      "D": "35"
    },
    "correct_answer": "D"
  }, {"id": 99, "difficulty": "hard", "question": "Two congruent regular polygons have exterior angle 18°. Find number of diagonals in each polygon.", "options": {"A": "135", "B": "152", "C": "170", "D": "189"}, "correct_answer": "C"},
    {"id": 100, "difficulty": "hard", "question": "In kite ABCD ≅ kite PQRS, AB = AD = 15 cm, BC = CD = 20 cm, diagonal AC = 24 cm. Find area of each kite.", "options": {"A": "180 cm²", "B": "240 cm²", "C": "300 cm²", "D": "360 cm²"}, "correct_answer": "B"}
  ,
 {"id":101,"difficulty":"easy","question":"Congruent figures always have the same:","options":{"A":"Position","B":"Color","C":"Shape and size","D":"Orientation"},"correct_answer":"C"},
    {"id":102,"difficulty":"easy","question":"If one figure can exactly cover another, the figures are:","options":{"A":"Similar","B":"Congruent","C":"Equivalent","D":"Parallel"},"correct_answer":"B"},
    {"id":103,"difficulty":"easy","question":"Congruence does not depend on:","options":{"A":"Size","B":"Shape","C":"Orientation","D":"Position"},"correct_answer":"D"},
    {"id":104,"difficulty":"easy","question":"Two congruent figures may face in:","options":{"A":"Same direction only","B":"Opposite directions","C":"Different sizes","D":"Different shapes"},"correct_answer":"B"},
    {"id":105,"difficulty":"easy","question":"If two figures are congruent, their corresponding sides are:","options":{"A":"Proportional","B":"Parallel","C":"Equal","D":"Perpendicular"},"correct_answer":"C"},
    {"id":106,"difficulty":"easy","question":"Congruent figures remain congruent after:","options":{"A":"Stretching","B":"Shrinking","C":"Rotation","D":"Resizing"},"correct_answer":"C"},
    {"id":107,"difficulty":"easy","question":"Which motion slides a figure without turning it?","options":{"A":"Rotation","B":"Reflection","C":"Translation","D":"Dilation"},"correct_answer":"C"},
    {"id":108,"difficulty":"easy","question":"If two figures are congruent, their boundaries have:","options":{"A":"Different lengths","B":"Same length","C":"Different shapes","D":"No relation"},"correct_answer":"B"},
    {"id":109,"difficulty":"easy","question":"Congruence compares figures based on:","options":{"A":"Area only","B":"Perimeter only","C":"Exact match","D":"Proportion"},"correct_answer":"C"},
    {"id":110,"difficulty":"easy","question":"If two objects are congruent, one is a ______ of the other.","options":{"A":"Scaled image","B":"Copy","C":"Reflection only","D":"Rotation only"},"correct_answer":"B"},
    {"id":111,"difficulty":"easy","question":"Congruence means figures can be matched by:","options":{"A":"Bending","B":"Cutting","C":"Rigid motion","D":"Stretching"},"correct_answer":"C"},
    {"id":112,"difficulty":"easy","question":"Congruent figures always have same:","options":{"A":"Orientation","B":"Area","C":"Position","D":"Color"},"correct_answer":"B"},
    {"id":113,"difficulty":"easy","question":"Two shapes are congruent if they are:","options":{"A":"Same size only","B":"Same shape only","C":"Same shape and size","D":"Similar"},"correct_answer":"C"},
    {"id":114,"difficulty":"easy","question":"Which of the following keeps a figure congruent?","options":{"A":"Dilation","B":"Stretching","C":"Reflection","D":"Rescaling"},"correct_answer":"C"},
    {"id":115,"difficulty":"easy","question":"Congruence ignores which feature?","options":{"A":"Length","B":"Angle","C":"Orientation","D":"Shape"},"correct_answer":"C"},
    {"id":116,"difficulty":"easy","question":"Two congruent figures placed exactly on each other will:","options":{"A":"Overlap partially","B":"Coincide completely","C":"Not overlap","D":"Change shape"},"correct_answer":"B"},
    {"id":117,"difficulty":"easy","question":"Congruence is about exact:","options":{"A":"Similarity","B":"Equality","C":"Proportion","D":"Comparison"},"correct_answer":"B"},
    {"id":118,"difficulty":"easy","question":"If figures are congruent, their corresponding angles are:","options":{"A":"Supplementary","B":"Complementary","C":"Equal","D":"Proportional"},"correct_answer":"C"},
    {"id":119,"difficulty":"easy","question":"Congruence can be checked using:","options":{"A":"Rigid movements","B":"Stretching","C":"Shrinking","D":"Skewing"},"correct_answer":"A"},
    {"id":120,"difficulty":"easy","question":"Congruent figures may look different because of:","options":{"A":"Size","B":"Shape","C":"Position","D":"Area"},"correct_answer":"C"},

    {"id":121,"difficulty":"medium","question":"Which transformation preserves congruence but changes orientation?","options":{"A":"Translation","B":"Rotation","C":"Reflection","D":"Dilation"},"correct_answer":"C"},
    {"id":122,"difficulty":"medium","question":"If two figures are congruent, which ratio is always 1?","options":{"A":"Area ratio","B":"Side ratio","C":"Angle ratio","D":"All of these"},"correct_answer":"D"},
    {"id":123,"difficulty":"medium","question":"Congruence is an equivalence relation because it is reflexive, symmetric and:","options":{"A":"Additive","B":"Multiplicative","C":"Transitive","D":"Commutative"},"correct_answer":"C"},
    {"id":124,"difficulty":"medium","question":"If A ≅ B and B ≅ C, then A ≅ C shows which property?","options":{"A":"Reflexive","B":"Symmetric","C":"Transitive","D":"Identity"},"correct_answer":"C"},
    {"id":125,"difficulty":"medium","question":"Which change breaks congruence but keeps similarity?","options":{"A":"Rotation","B":"Reflection","C":"Translation","D":"Dilation"},"correct_answer":"D"},
     {
    "id": 126,
    "difficulty": "medium",
    "question": "If LM = (6x−8) cm and NO = (4x+6) cm are congruent, find LM.",
    "options": {
      "A": "16 cm",
      "B": "18 cm",
      "C": "20 cm",
      "D": "34 cm"
    },
    "correct_answer": "D"
  }, {"id":127,"difficulty":"medium","question":"Which pair can be congruent?","options":{"A":"Two squares of different sizes","B":"Two circles of equal radius","C":"Two rectangles with same area","D":"Two triangles with equal angles"},"correct_answer":"B"},
    {"id":128,"difficulty":"medium","question":"Congruence preserves which geometric property?","options":{"A":"Distance","B":"Angle","C":"Area","D":"All of these"},"correct_answer":"D"},
    {"id":129,"difficulty":"medium","question":"If two figures differ only by turning, they are related by:","options":{"A":"Reflection","B":"Translation","C":"Rotation","D":"Dilation"},"correct_answer":"C"},
    {"id":130,"difficulty":"medium","question":"Two congruent polygons must have same number of:","options":{"A":"Diagonals","B":"Vertices","C":"Angles","D":"All of these"},"correct_answer":"D"},

   
     {
    "id": 131,
    "difficulty": "hard",
    "question": "In ΔABC ≅ ΔPQR, AB = (2x+4) cm, PQ = 18 cm, BC = (3y−2) cm, QR = 25 cm. Find x+y.",
    "options": {
      "A": "10",
      "B": "12",
      "C": "14",
      "D": "16"
    },
    "correct_answer": "D"
  }, {"id":132,"difficulty":"hard","question":"A shape is reflected and then translated. Compared to original, the new shape is:","options":{"A":"Similar","B":"Congruent","C":"Dilated","D":"Distorted"},"correct_answer":"B"},
    {"id":133,"difficulty":"hard","question":"Which sequence of transformations keeps congruence intact?","options":{"A":"Rotation → Dilation","B":"Reflection → Translation","C":"Dilation → Rotation","D":"Stretching → Reflection"},"correct_answer":"B"},
    {"id":134,"difficulty":"hard","question":"If two figures have equal area but are not congruent, they must differ in:","options":{"A":"Shape","B":"Size","C":"Position","D":"Orientation"},"correct_answer":"A"},
    {"id":135,"difficulty":"hard","question":"Which statement is NOT sufficient to claim congruence?","options":{"A":"Equal corresponding sides","B":"Equal corresponding angles","C":"Equal perimeters","D":"Rigid motion possible"},"correct_answer":"C"},
     {
    "id": 136,
    "difficulty": "hard",
    "question": "Two congruent equilateral triangles have area 36√3 cm². Find side length.",
    "options": {
      "A": "6 cm",
      "B": "8 cm",
      "C": "10 cm",
      "D": "12 cm"
    },
    "correct_answer": "D"
  },  {
    "id": 137,
    "difficulty": "hard",
    "question": "In trapezium ABCD ≅ trapezium PQRS, parallel sides are 12 cm and 20 cm, legs 10 cm each. Find perimeter.",
    "options": {
      "A": "52 cm",
      "B": "60 cm",
      "C": "64 cm",
      "D": "72 cm"
    },
    "correct_answer": "A"
  },  {
    "id": 138,
    "difficulty": "hard",
    "question": "Two congruent circles have area 308 cm² (π=22/7). Find diameter.",
    "options": {
      "A": "7 cm",
      "B": "10 cm",
      "C": "14 cm",
      "D": "14√2 cm"
    },
    "correct_answer": "D"
  },
  {
    "id": 139,
    "difficulty": "hard",
    "question": "In ΔXYZ ≅ ΔLMN, XY = (3p+1) cm, LM = 22 cm, YZ = (4q−3) cm, MN = 29 cm. Find p+q.",
    "options": {
      "A": "12",
      "B": "14",
      "C": "16",
      "D": "15"
    },
    "correct_answer": "D"
  },  {"id":140,"difficulty":"hard","question":"If two figures are congruent, their corresponding diagonals are:","options":{"A":"Equal","B":"Parallel","C":"Perpendicular","D":"Different"},"correct_answer":"A"},
    {"id":141,"difficulty":"hard","question":"Which real-life process relies most on congruence?","options":{"A":"Map scaling","B":"Photocopying","C":"Manufacturing parts","D":"Model drawing"},"correct_answer":"C"},
   {
    "id": 142,
    "difficulty": "hard",
    "question": "Two congruent isosceles triangles have base 16 cm and equal sides 10 cm. Find height.",
    "options": {
      "A": "6 cm",
      "B": "8 cm",
      "C": "10 cm",
      "D": "12 cm"
    },
    "correct_answer": "A"
  }, {"id":143,"difficulty":"hard","question":"If two shapes are congruent, their corresponding medians are:","options":{"A":"Equal","B":"Parallel","C":"Perpendicular","D":"Proportional"},"correct_answer":"A"},
    {"id":144,"difficulty":"hard","question":"Congruence ensures equality of all corresponding:","options":{"A":"Sides","B":"Angles","C":"Distances","D":"All"},"correct_answer":"D"},
    {"id":145,"difficulty":"hard","question":"Which breaks congruence but keeps angles equal?","options":{"A":"Rotation","B":"Reflection","C":"Translation","D":"Dilation"},"correct_answer":"D"},
    {
    "id": 146,
    "difficulty": "hard",
    "question": "Two congruent circles have radius 10.5 cm. Find circumference (π=22/7).",
    "options": {
      "A": "44 cm",
      "B": "66 cm",
      "C": "88 cm",
      "D": "132 cm"
    },
    "correct_answer": "B"
  }, {"id":147,"difficulty":"hard","question":"If congruence is preserved, then distances between any two points are:","options":{"A":"Changed","B":"Proportional","C":"Equal","D":"Reduced"},"correct_answer":"C"},
    {"id":148,"difficulty":"hard","question":"Which property of congruence allows A ≅ A?","options":{"A":"Symmetric","B":"Transitive","C":"Reflexive","D":"Associative"},"correct_answer":"C"},
    {"id":149,"difficulty":"hard","question":"Congruence differs from similarity mainly in terms of:","options":{"A":"Angles","B":"Proportions","C":"Scale","D":"Exactness"},"correct_answer":"D"},
    {
    "id": 150,
    "difficulty": "hard",
    "question": "Congruent rectangles have diagonal 13 cm and one side 5 cm. Find the other side.",
    "options": {
      "A": "8 cm",
      "B": "10 cm",
      "C": "12 cm",
      "D": "15 cm"
    },
    "correct_answer": "C"
  }]
}