{
  "title": "Congruent Line Segments - Grade 7 CBSE",
  "total_questions": 150,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "What does it mean for two line segments to be congruent?", "options": {"A": "They are parallel", "B": "They have equal length", "C": "They are perpendicular", "D": "They intersect"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "If AB = 5 cm and CD = 5 cm, then AB and CD are:", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Congruent", "D": "Collinear"}, "correct_answer": "C"},
    {"id": 3, "difficulty": "easy", "question": "Which symbol represents line segment congruence?", "options": {"A": "=", "B": "≈", "C": "≅", "D": "∼"}, "correct_answer": "C"},
    {"id": 4, "difficulty": "easy", "question": "If AB ≅ CD, then:", "options": {"A": "AB is parallel to CD", "B": "AB = CD", "C": "AB intersects CD", "D": "AB is perpendicular to CD"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "All sides of an equilateral triangle are:", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Congruent", "D": "Different lengths"}, "correct_answer": "C"},
    {"id": 6, "difficulty": "easy", "question": "If PQ ≅ RS and PQ = 8 cm, then RS =", "options": {"A": "4 cm", "B": "8 cm", "C": "12 cm", "D": "16 cm"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "In a square, all sides are:", "options": {"A": "Different lengths", "B": "Congruent", "C": "Parallel only", "D": "Perpendicular only"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "If two line segments are congruent, they can have:", "options": {"A": "Different lengths", "B": "Same length but different positions", "C": "Same position only", "D": "Same direction only"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "In a rhombus, all sides are:", "options": {"A": "Different lengths", "B": "Congruent", "C": "Parallel only", "D": "Perpendicular only"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "If AB ≅ BC and BC ≅ CD, then:", "options": {"A": "AB ≅ CD", "B": "AB is parallel to CD", "C": "A, B, C, D are collinear", "D": "AB ⊥ CD"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "Opposite sides of a rectangle are:", "options": {"A": "Congruent", "B": "Perpendicular", "C": "Different lengths", "D": "Not parallel"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "If line segment AB is congruent to line segment CD, we write:", "options": {"A": "AB = CD", "B": "AB ≅ CD", "C": "Both A and B", "D": "AB ≈ CD"}, "correct_answer": "C"},
    {"id": 13, "difficulty": "easy", "question": "In an isosceles triangle, the equal sides are:", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Congruent", "D": "Different"}, "correct_answer": "C"},
    {"id": 14, "difficulty": "easy", "question": "If two line segments have equal lengths, they are:", "options": {"A": "Always parallel", "B": "Always perpendicular", "C": "Congruent", "D": "Always intersecting"}, "correct_answer": "C"},
    {"id": 15, "difficulty": "easy", "question": "In a parallelogram, opposite sides are:", "options": {"A": "Congruent", "B": "Perpendicular", "C": "Different lengths", "D": "Not parallel"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "If AB = 7 cm and you want CD congruent to AB, then CD should be:", "options": {"A": "3.5 cm", "B": "7 cm", "C": "10.5 cm", "D": "14 cm"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "All radii of the same circle are:", "options": {"A": "Different lengths", "B": "Congruent", "C": "Parallel", "D": "Perpendicular"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "If two line segments are congruent, their midpoints divide them into:", "options": {"A": "Equal halves", "B": "Unequal halves", "C": "Thirds", "D": "Quarters"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "In a kite, which sides are congruent?", "options": {"A": "All sides", "B": "Opposite sides", "C": "Adjacent sides", "D": "No sides are congruent"}, "correct_answer": "C"},
    {"id": 20, "difficulty": "easy", "question": "If AB ≅ CD and CD ≅ EF, then AB and EF are:", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Congruent", "D": "Collinear"}, "correct_answer": "C"},
    
    {"id": 21, "difficulty": "medium", "question": "In ΔABC ≅ ΔPQR, if AB = 8 cm, what is PQ?", "options": {"A": "4 cm", "B": "6 cm", "C": "8 cm", "D": "10 cm"}, "correct_answer": "C"},
    {"id": 22, "difficulty": "medium", "question": "If AB = (3x+2) cm and CD = (2x+8) cm are congruent, find x.", "options": {"A": "2", "B": "4", "C": "6", "D": "8"}, "correct_answer": "C"},
    {"id": 23, "difficulty": "medium", "question": "In square ABCD, side = 5 cm. If square PQRS ≅ square ABCD, what is side of PQRS?", "options": {"A": "2.5 cm", "B": "5 cm", "C": "7.5 cm", "D": "10 cm"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "Rectangle has length 12 cm, width 8 cm. Congruent rectangle has:", "options": {"A": "Length 6 cm, width 4 cm", "B": "Length 12 cm, width 8 cm", "C": "Length 16 cm, width 12 cm", "D": "Length 24 cm, width 16 cm"}, "correct_answer": "B"},
    {"id": 25, "difficulty": "medium", "question": "In rhombus, all sides are 7 cm. Congruent rhombus has perimeter:", "options": {"A": "14 cm", "B": "21 cm", "C": "28 cm", "D": "35 cm"}, "correct_answer": "C"},
     {
    "id": 26,
    "difficulty": "medium",
    "question": "If AB ≅ CD and AB = 2x-3, CD = x+9, find AB length.",
    "options": {
      "A": "12 cm",
      "B": "15 cm",
      "C": "18 cm",
      "D": "21 cm"
    },
    "correct_answer": "D"
  }, {"id": 27, "difficulty": "medium", "question": "In regular hexagon with side 4 cm, congruent hexagon has perimeter:", "options": {"A": "12 cm", "B": "18 cm", "C": "24 cm", "D": "30 cm"}, "correct_answer": "C"},
    {"id": 28, "difficulty": "medium", "question": "Two circles are congruent. If radius of first is 5 cm, diameter of second is:", "options": {"A": "2.5 cm", "B": "5 cm", "C": "10 cm", "D": "20 cm"}, "correct_answer": "C"},
    {"id": 29, "difficulty": "medium", "question": "In ΔABC ≅ ΔXYZ, if BC = 3y-4 and YZ = 17, find y.", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "C"},
    {"id": 30, "difficulty": "medium", "question": "Isosceles triangle has equal sides 10 cm, base 12 cm. Congruent triangle has perimeter:", "options": {"A": "24 cm", "B": "30 cm", "C": "32 cm", "D": "36 cm"}, "correct_answer": "C"},
    {"id": 31, "difficulty": "medium", "question": "If PQ = (4x-6) cm, RS = (2x+18) cm are congruent, find x.", "options": {"A": "6", "B": "8", "C": "10", "D": "12"}, "correct_answer": "D"},
    {"id": 32, "difficulty": "medium", "question": "In parallelogram, sides are 8 cm and 12 cm. Congruent parallelogram has area:", "options": {"A": "Same", "B": "Double", "C": "Half", "D": "Cannot determine without height"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "Two line segments AB and CD are congruent. If AB is divided into 3 equal parts, CD can be divided into:", "options": {"A": "2 equal parts", "B": "3 equal parts of same length", "C": "4 equal parts", "D": "Different length parts"}, "correct_answer": "B"},
    {"id": 34, "difficulty": "medium", "question": "In trapezoid with parallel sides 10 cm and 16 cm, non-parallel sides 5 cm each. Congruent trapezoid has:", "options": {"A": "Same measurements", "B": "Proportional measurements", "C": "Double measurements", "D": "Half measurements"}, "correct_answer": "A"},
    {"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": "40 cm"}, "correct_answer": "C"},
     {
    "id": 36,
    "difficulty": "medium",
    "question": "Equilateral triangle side 9 cm. Congruent triangle has height:",
    "options": {
      "A": "4.5√3 cm",
      "B": "6√3 cm",
      "C": "7.5√3 cm",
      "D": "9√3 cm"
    },
    "correct_answer": "A"
  }, {"id": 37, "difficulty": "medium", "question": "In rectangle, diagonal = 13 cm, one side = 5 cm. Congruent rectangle has other side:", "options": {"A": "8 cm", "B": "10 cm", "C": "12 cm", "D": "15 cm"}, "correct_answer": "C"},
    {"id": 38, "difficulty": "medium", "question": "If LM = (5y-8) cm, NO = (3y+16) cm are congruent, find y.", "options": {"A": "8", "B": "10", "C": "12", "D": "14"}, "correct_answer": "C"},
    {"id": 39, "difficulty": "medium", "question": "Two circles congruent, circumference = 44 cm (π=22/7). Radius =", "options": {"A": "3.5 cm", "B": "7 cm", "C": "10.5 cm", "D": "14 cm"}, "correct_answer": "B"},
    {
    "id": 40,
    "difficulty": "medium",
    "question": "In ΔPQR ≅ ΔSTU, PQ = 2x+3, ST = 15, find x.",
    "options": {
      "A": "4",
      "B": "5",
      "C": "6",
      "D": "7"
    },
    "correct_answer": "C"
  },  {"id": 41, "difficulty": "medium", "question": "Square has diagonal 10√2 cm. Congruent square has side:", "options": {"A": "5 cm", "B": "8 cm", "C": "10 cm", "D": "12 cm"}, "correct_answer": "C"},
    {"id": 42, "difficulty": "medium", "question": "If AB = CD and CD = EF, then:", "options": {"A": "AB = EF", "B": "AB || EF", "C": "AB ⊥ EF", "D": "A, B, E, F collinear"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "In rhombus, diagonals 10 cm and 24 cm. Congruent rhombus has side:", "options": {"A": "10 cm", "B": "12 cm", "C": "13 cm", "D": "15 cm"}, "correct_answer": "C"},
     {
    "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": "Two congruent triangles have sides 6 cm, 8 cm, 10 cm. Their areas are:", "options": {"A": "Equal", "B": "Different", "C": "Proportional", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "medium", "question": "In regular pentagon side 6 cm, congruent pentagon has perimeter:", "options": {"A": "20 cm", "B": "24 cm", "C": "30 cm", "D": "36 cm"}, "correct_answer": "C"},
      {
    "id": 47,
    "difficulty": "medium",
    "question": "If AB ≅ BC ≅ CD, and AB = 2x+1, CD = x+10, find length.",
    "options": {
      "A": "13 cm",
      "B": "15 cm",
      "C": "17 cm",
      "D": "19 cm"
    },
    "correct_answer": "D"
  },  {"id": 48, "difficulty": "medium", "question": "Circle radius 14 cm, congruent circle has area (π=22/7):", "options": {"A": "154 cm²", "B": "308 cm²", "C": "616 cm²", "D": "1232 cm²"}, "correct_answer": "C"},
      {
    "id": 49,
    "difficulty": "medium",
    "question": "In ΔABC ≅ ΔXYZ, AC = 4y-7, XZ = 25, find y.",
    "options": {
      "A": "6",
      "B": "7",
      "C": "8",
      "D": "9"
    },
    "correct_answer": "C"
  }, {"id": 50, "difficulty": "medium", "question": "Isosceles trapezoid has bases 8 cm, 14 cm, legs 5 cm. Congruent trapezoid has perimeter:", "options": {"A": "24 cm", "B": "28 cm", "C": "32 cm", "D": "36 cm"}, "correct_answer": "C"},
    {"id": 51, "difficulty": "medium", "question": "If MN = (3x+5) cm, OP = (5x-15) cm are congruent, find x.", "options": {"A": "5", "B": "8", "C": "10", "D": "12"}, "correct_answer": "C"},
    {"id": 52, "difficulty": "medium", "question": "Two squares congruent. One has area 81 cm², other has side:", "options": {"A": "6 cm", "B": "7 cm", "C": "8 cm", "D": "9 cm"}, "correct_answer": "D"},
    {"id": 53, "difficulty": "medium", "question": "In parallelogram, sides 9 cm and 12 cm, included angle 60°. Congruent parallelogram has same:", "options": {"A": "Sides and angle", "B": "Area only", "C": "Perimeter only", "D": "Diagonal only"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "medium", "question": "If AB = CD, and AB = 3/4 of 20 cm, then CD =", "options": {"A": "12 cm", "B": "15 cm", "C": "18 cm", "D": "20 cm"}, "correct_answer": "B"},
    {"id": 55, "difficulty": "medium", "question": "Two congruent rectangles have perimeter 40 cm. If length 12 cm, width =", "options": {"A": "4 cm", "B": "6 cm", "C": "8 cm", "D": "10 cm"}, "correct_answer": "C"},
    {"id": 56, "difficulty": "medium", "question": "In ΔPQR ≅ ΔLMN, QR = 3z-2, MN = 19, find z.", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "C"},
    {"id": 57, "difficulty": "medium", "question": "Equilateral triangle perimeter 36 cm. Congruent triangle has side:", "options": {"A": "9 cm", "B": "10 cm", "C": "11 cm", "D": "12 cm"}, "correct_answer": "D"},
      {
    "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": "Two circles congruent, area 154 cm² (π=22/7). Diameter =", "options": {"A": "7 cm", "B": "14 cm", "C": "21 cm", "D": "28 cm"}, "correct_answer": "B"},
    {"id": 60, "difficulty": "medium", "question": "In kite, equal sides 13 cm, other equal sides 10 cm. Congruent kite has perimeter:", "options": {"A": "36 cm", "B": "42 cm", "C": "46 cm", "D": "52 cm"}, "correct_answer": "C"},
    {"id": 61, "difficulty": "medium", "question": "If AB = (2x+8) cm, CD = (5x-7) cm are congruent, find x.", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "C"},
    {"id": 62, "difficulty": "medium", "question": "Two congruent right triangles have legs 9 cm, 12 cm. Hypotenuse =", "options": {"A": "13 cm", "B": "15 cm", "C": "17 cm", "D": "20 cm"}, "correct_answer": "B"},
    {"id": 63, "difficulty": "medium", "question": "In regular octagon side 5 cm, congruent octagon has perimeter:", "options": {"A": "30 cm", "B": "35 cm", "C": "40 cm", "D": "45 cm"}, "correct_answer": "C"},
    {"id": 64, "difficulty": "medium", "question": "If LM = NO and NO = PQ, then:", "options": {"A": "LM = PQ", "B": "LM || PQ", "C": "LM ⊥ PQ", "D": "L, M, P, Q collinear"}, "correct_answer": "A"},
    {"id": 65, "difficulty": "medium", "question": "Two congruent isosceles triangles have base 16 cm, equal sides 10 cm. Height =", "options": {"A": "4 cm", "B": "5 cm", "C": "6 cm", "D": "8 cm"}, "correct_answer": "C"},
    {"id": 66, "difficulty": "medium", "question": "In ΔABC ≅ ΔXYZ, BC = 5x-4, YZ = 26, find x.", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "C"},
    {"id": 67, "difficulty": "medium", "question": "Square area 64 cm². Congruent square has diagonal:", "options": {"A": "8 cm", "B": "8√2 cm", "C": "12 cm", "D": "16 cm"}, "correct_answer": "B"},
     {
    "id": 68,
    "difficulty": "medium",
    "question": "If RS = (4x-9) cm, TU = (6x-21) cm are congruent, find length.",
    "options": {
      "A": "12 cm",
      "B": "15 cm",
      "C": "18 cm",
      "D": "21 cm"
    },
    "correct_answer": "B"
  }, {"id": 69, "difficulty": "medium", "question": "Two congruent circles have circumference 66 cm (π=22/7). Area =", "options": {"A": "346.5 cm²", "B": "380 cm²", "C": "415 cm²", "D": "450 cm²"}, "correct_answer": "A"},
    {"id": 70, "difficulty": "medium", "question": "In rhombus, side 13 cm, one diagonal 10 cm. Congruent rhombus has other diagonal:", "options": {"A": "12 cm", "B": "18 cm", "C": "20 cm", "D": "24 cm"}, "correct_answer": "D"},
    {"id": 71, "difficulty": "medium", "question": "If AB ≅ BC ≅ CA, triangle is:", "options": {"A": "Isosceles", "B": "Equilateral", "C": "Right", "D": "Scalene"}, "correct_answer": "B"},
    {"id": 72, "difficulty": "medium", "question": "Two congruent rectangles have area 96 cm². If length 12 cm, width =", "options": {"A": "6 cm", "B": "8 cm", "C": "10 cm", "D": "12 cm"}, "correct_answer": "B"},
    {"id": 73, "difficulty": "medium", "question": "In ΔPQR ≅ ΔSTU, PR = 3y+4, SU = 25, find y.", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "C"},
    {"id": 74, "difficulty": "medium", "question": "Regular hexagon side 7 cm. Congruent hexagon has distance between parallel sides:", "options": {"A": "7√3 cm", "B": "10.5 cm", "C": "12 cm", "D": "14 cm"}, "correct_answer": "A"},
    {"id": 75, "difficulty": "medium", "question": "If PQ = RS and RS = 2/3 of 27 cm, then PQ =", "options": {"A": "12 cm", "B": "15 cm", "C": "18 cm", "D": "21 cm"}, "correct_answer": "C"},
    {"id": 76, "difficulty": "medium", "question": "Two congruent isosceles triangles have perimeter 32 cm. If base 12 cm, equal side =", "options": {"A": "8 cm", "B": "9 cm", "C": "10 cm", "D": "11 cm"}, "correct_answer": "C"},
    {"id": 77, "difficulty": "medium", "question": "In parallelogram, sides 15 cm and 20 cm, diagonal 25 cm. Congruent parallelogram has:", "options": {"A": "Same diagonal", "B": "Different diagonal", "C": "Cannot determine", "D": "Double diagonal"}, "correct_answer": "A"},
     {
    "id": 78,
    "difficulty": "medium",
    "question": "If AB = (5x-12) cm, CD = (7x-30) cm are congruent, find x.",
    "options": {
      "A": "6",
      "B": "7",
      "C": "8",
      "D": "9"
    },
    "correct_answer": "D"
  }, {"id": 79, "difficulty": "medium", "question": "Two congruent circles have area 616 cm² (π=22/7). Circumference =", "options": {"A": "44 cm", "B": "66 cm", "C": "88 cm", "D": "110 cm"}, "correct_answer": "C"},
    {"id": 80, "difficulty": "medium", "question": "In trapezium, parallel sides 10 cm, 18 cm, non-parallel sides 7 cm each. Congruent trapezium has area if height 6 cm:", "options": {"A": "60 cm²", "B": "72 cm²", "C": "84 cm²", "D": "96 cm²"}, "correct_answer": "C"},
    
    {"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": "C"},
    {"id": 82, "difficulty": "hard", "question": "Two congruent regular polygons have side length 8 cm. If each interior angle is 135°, find number of sides and perimeter.", "options": {"A": "8 sides, 64 cm", "B": "10 sides, 80 cm", "C": "12 sides, 96 cm", "D": "15 sides, 120 cm"}, "correct_answer": "A"},
    {"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": "B"},
    {"id": 84, "difficulty": "hard", "question": "Two congruent circles intersect. Distance between centers is 12 cm. If radius is 10 cm, find length of common chord.", "options": {"A": "12 cm", "B": "14 cm", "C": "16 cm", "D": "18 cm"}, "correct_answer": "C"},
    {"id": 85, "difficulty": "hard", "question": "In rhombus ABCD ≅ rhombus PQRS, diagonal AC = (3x+4) cm, PR = 28 cm, diagonal BD = (4y-5) cm, QS = 35 cm. Find x and y.", "options": {"A": "x=8, y=10", "B": "x=9, y=11", "C": "x=10, y=12", "D": "x=11, y=13"}, "correct_answer": "A"},
    {
    "id": 86,
    "difficulty": "hard",
    "question": "Two congruent isosceles triangles have perimeter 50 cm. Equal sides are 3 cm longer than base. Find area if height to base is 12 cm.",
    "options": {
      "A": "60 cm²",
      "B": "84 cm²",
      "C": "96 cm²",
      "D": "108 cm²"
    },
    "correct_answer": "C"
  },  {"id": 87, "difficulty": "hard", "question": "In trapezoid ABCD ≅ trapezoid PQRS, AB∥CD, PQ∥RS. AB = (2x+3) cm, PQ = 15 cm, CD = (3y-2) cm, RS = 22 cm, AD = (4z-1) cm, PS = 19 cm. Find x+y+z.", "options": {"A": "15", "B": "18", "C": "21", "D": "24"}, "correct_answer": "B"},
    {"id": 88, "difficulty": "hard", "question": "Two congruent regular hexagons have side 6 cm. They are placed side by side. Find perimeter of resulting figure.", "options": {"A": "60 cm", "B": "66 cm", "C": "72 cm", "D": "78 cm"}, "correct_answer": "C"},
    {"id": 89, "difficulty": "hard", "question": "In ΔXYZ ≅ ΔLMN, XY = (3p+2) cm, LM = 23 cm, YZ = (4q-3) cm, MN = 33 cm, ZX = (5r-4) cm, NL = 41 cm. Find p+q+r.", "options": {"A": "20", "B": "23", "C": "26", "D": "29"}, "correct_answer": "C"},
    {"id": 90, "difficulty": "hard", "question": "Two congruent sectors of circle have radius 14 cm and central angle 60°. Find area of each sector (π=22/7).", "options": {"A": "308/3 cm²", "B": "102.67 cm²", "C": "154/3 cm²", "D": "51.33 cm²"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "In kite ABCD ≅ kite PQRS, AB = AD = (2x+3) cm, PQ = 15 cm, BC = CD = (3y-2) cm, QR = 19 cm. Find x and y.", "options": {"A": "x=6, y=7", "B": "x=7, y=8", "C": "x=8, y=9", "D": "x=9, y=10"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "Two congruent cylinders have curved surface area 2640 cm² (π=22/7). If height is 20 cm, find radius.", "options": {"A": "14 cm", "B": "21 cm", "C": "28 cm", "D": "35 cm"}, "correct_answer": "B"},
    {"id": 93, "difficulty": "hard", "question": "In parallelogram ABCD ≅ parallelogram WXYZ, AB = (3a-2) cm, WX = 16 cm, BC = (4b+1) cm, XY = 25 cm. Find a and b.", "options": {"A": "a=6, b=6", "B": "a=7, b=7", "C": "a=8, b=8", "D": "a=9, b=9"}, "correct_answer": "A"},
    {"id": 94, "difficulty": "hard", "question": "Two congruent cones have slant height 17 cm and radius 8 cm. Find height.", "options": {"A": "12 cm", "B": "13 cm", "C": "14 cm", "D": "15 cm"}, "correct_answer": "D"},
    {"id": 95, "difficulty": "hard", "question": "In regular pentagon ABCDE ≅ regular pentagon PQRST, side AB = (2x+1) cm, side PQ = 15 cm. Find x and perimeter.", "options": {"A": "x=7, perimeter=75 cm", "B": "x=8, perimeter=80 cm", "C": "x=9, perimeter=85 cm", "D": "x=10, perimeter=90 cm"}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "Two congruent spheres have volume 38808/21 cm³ (π=22/7). Find surface area.", "options": {"A": "616 cm²", "B": "1232 cm²", "C": "1848 cm²", "D": "2464 cm²"}, "correct_answer": "A"},
    {"id": 97, "difficulty": "hard", "question": "In ΔABC ≅ ΔDEF, AB = (3m+2) cm, DE = 20 cm, BC = (4n-3) cm, EF = 29 cm, CA = (5p-4) cm, FD = 36 cm. Find m+n+p.", "options": {"A": "18", "B": "21", "C": "24", "D": "27"}, "correct_answer": "C"},
    {"id": 98, "difficulty": "hard", "question": "Two congruent regular polygons have exterior angle 18°. If side is 5 cm, find perimeter.", "options": {"A": "80 cm", "B": "90 cm", "C": "100 cm", "D": "110 cm"}, "correct_answer": "C"},
    {"id": 99, "difficulty": "hard", "question": "In trapezium ABCD ≅ trapezium PQRS with AB∥CD, PQ∥RS. AB = (2a+3) cm, PQ = 17 cm, BC = (3b-2) cm, QR = 22 cm, CD = (4c-1) cm, RS = 31 cm. Find a+b+c.", "options": {"A": "20", "B": "23", "C": "26", "D": "29"}, "correct_answer": "B"},
    {"id": 100, "difficulty": "hard", "question": "Two congruent pyramids have square base side 12 cm and slant height 10 cm. Find lateral surface area.", "options": {"A": "240 cm²", "B": "288 cm²", "C": "336 cm²", "D": "384 cm²"}, "correct_answer": "A"}
  ,
  {"id":101,"difficulty":"easy","question":"If two line segments each measure 9 cm, they are:","options":{"A":"Parallel","B":"Congruent","C":"Perpendicular","D":"Intersecting"},"correct_answer":"B"},
    {"id":102,"difficulty":"easy","question":"Which property defines congruent line segments?","options":{"A":"Same direction","B":"Same midpoint","C":"Same length","D":"Same slope"},"correct_answer":"C"},
    {"id":103,"difficulty":"easy","question":"All sides of a regular pentagon are:","options":{"A":"Unequal","B":"Parallel","C":"Congruent","D":"Perpendicular"},"correct_answer":"C"},
    {"id":104,"difficulty":"easy","question":"If AB ≅ CD and AB = 11 cm, then CD equals:","options":{"A":"5.5 cm","B":"11 cm","C":"22 cm","D":"33 cm"},"correct_answer":"B"},
    {"id":105,"difficulty":"easy","question":"Congruent line segments may lie in:","options":{"A":"Same position only","B":"Different positions","C":"Same direction only","D":"Same line only"},"correct_answer":"B"},
    {"id":106,"difficulty":"easy","question":"In a regular triangle, all sides are:","options":{"A":"Different","B":"Congruent","C":"Parallel","D":"Perpendicular"},"correct_answer":"B"},
    {"id":107,"difficulty":"easy","question":"If two line segments have equal measures, we call them:","options":{"A":"Parallel","B":"Collinear","C":"Congruent","D":"Adjacent"},"correct_answer":"C"},
    {"id":108,"difficulty":"easy","question":"All diameters of the same circle are:","options":{"A":"Unequal","B":"Congruent","C":"Parallel","D":"Skew"},"correct_answer":"B"},
    {"id":109,"difficulty":"easy","question":"In a square, how many sides are congruent?","options":{"A":"2","B":"3","C":"4","D":"None"},"correct_answer":"C"},
    {"id":110,"difficulty":"easy","question":"If PQ ≅ RS and RS ≅ TU, then PQ and TU are:","options":{"A":"Parallel","B":"Congruent","C":"Perpendicular","D":"Intersecting"},"correct_answer":"B"},
    {"id":111,"difficulty":"easy","question":"Opposite sides of a rhombus are:","options":{"A":"Unequal","B":"Congruent","C":"Perpendicular","D":"Non-parallel"},"correct_answer":"B"},
    {"id":112,"difficulty":"easy","question":"If line segment LM = 6 cm and NO is congruent to LM, then NO is:","options":{"A":"3 cm","B":"6 cm","C":"9 cm","D":"12 cm"},"correct_answer":"B"},
    {"id":113,"difficulty":"easy","question":"Which symbol is used for line segment congruence?","options":{"A":"=","B":"≈","C":"≅","D":"∼"},"correct_answer":"C"},
    {"id":114,"difficulty":"easy","question":"In an isosceles triangle, the equal sides are:","options":{"A":"Parallel","B":"Congruent","C":"Unequal","D":"Perpendicular"},"correct_answer":"B"},
    {"id":115,"difficulty":"easy","question":"If two segments are congruent, their lengths are:","options":{"A":"Different","B":"Equal","C":"Proportional","D":"Opposite"},"correct_answer":"B"},
    {"id":116,"difficulty":"easy","question":"All sides of a regular hexagon are:","options":{"A":"Different","B":"Congruent","C":"Parallel","D":"Perpendicular"},"correct_answer":"B"},
    {"id":117,"difficulty":"easy","question":"If AB = CD = EF, then all three segments are:","options":{"A":"Parallel","B":"Congruent","C":"Collinear","D":"Intersecting"},"correct_answer":"B"},
    {"id":118,"difficulty":"easy","question":"Two congruent line segments can have different:","options":{"A":"Length","B":"Midpoints","C":"Position","D":"Measures"},"correct_answer":"C"},
    {"id":119,"difficulty":"easy","question":"All sides of an equilateral triangle are congruent because they have:","options":{"A":"Same angle","B":"Same length","C":"Same slope","D":"Same direction"},"correct_answer":"B"},
    {"id":120,"difficulty":"easy","question":"If a segment is divided into two equal parts, those parts are:","options":{"A":"Unequal","B":"Congruent","C":"Parallel","D":"Skew"},"correct_answer":"B"},

    {"id":121,"difficulty":"medium","question":"If AB = (4x+2) cm and CD = (2x+14) cm are congruent, find x.","options":{"A":"4","B":"6","C":"8","D":"10"},"correct_answer":"C"},
    {"id":122,"difficulty":"medium","question":"A square has side 7 cm. A congruent square has perimeter:","options":{"A":"14 cm","B":"21 cm","C":"28 cm","D":"35 cm"},"correct_answer":"C"},
    {"id":123,"difficulty":"medium","question":"Two congruent circles have radius 6 cm. Find the diameter.","options":{"A":"6 cm","B":"9 cm","C":"12 cm","D":"18 cm"},"correct_answer":"C"},
    {"id":124,"difficulty":"medium","question":"In ΔABC ≅ ΔPQR, if BC = 5y+3 and QR = 28, find y.","options":{"A":"4","B":"5","C":"6","D":"7"},"correct_answer":"C"},
    {"id":125,"difficulty":"medium","question":"A rhombus has all sides 10 cm. Find the perimeter of a congruent rhombus.","options":{"A":"20 cm","B":"30 cm","C":"40 cm","D":"50 cm"},"correct_answer":"C"},
    {"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":"22 cm"},"correct_answer":"C"},
    {"id":127,"difficulty":"medium","question":"An equilateral triangle has perimeter 24 cm. Find side of a congruent triangle.","options":{"A":"6 cm","B":"8 cm","C":"10 cm","D":"12 cm"},"correct_answer":"B"},
    {"id":128,"difficulty":"medium","question":"Two congruent rectangles have length 14 cm and width 6 cm. Find area.","options":{"A":"40 cm²","B":"60 cm²","C":"84 cm²","D":"120 cm²"},"correct_answer":"C"},
    {"id":129,"difficulty":"medium","question":"If PQ = RS and RS = 18 cm, what is PQ?","options":{"A":"9 cm","B":"12 cm","C":"18 cm","D":"36 cm"},"correct_answer":"C"},
    {"id":130,"difficulty":"medium","question":"A regular octagon has side 5 cm. Find perimeter of a congruent octagon.","options":{"A":"30 cm","B":"35 cm","C":"40 cm","D":"45 cm"},"correct_answer":"C"},
{"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":"C"},
    {"id":132,"difficulty":"hard","question":"Two congruent squares have diagonal 10√2 cm. Find total perimeter of both.","options":{"A":"40 cm","B":"80 cm","C":"120 cm","D":"160 cm"},"correct_answer":"B"},
    {"id":133,"difficulty":"hard","question":"In a congruent pair of isosceles triangles, equal sides are 13 cm and base is 10 cm. Find perimeter.","options":{"A":"32 cm","B":"34 cm","C":"36 cm","D":"38 cm"},"correct_answer":"C"},
    {"id":134,"difficulty":"hard","question":"Two congruent circles have circumference 88 cm (π=22/7). Find radius.","options":{"A":"7 cm","B":"14 cm","C":"21 cm","D":"28 cm"},"correct_answer":"B"},
    {"id":135,"difficulty":"hard","question":"In rhombus ABCD ≅ rhombus PQRS, diagonals are 10 cm and 24 cm. Find side length.","options":{"A":"11 cm","B":"12 cm","C":"13 cm","D":"14 cm"},"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":"B"},
    {"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":"C"},
    {"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":"21 cm"},"correct_answer":"C"},
    {"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":"18"},"correct_answer":"C"},
    {"id":140,"difficulty":"hard","question":"Two congruent regular hexagons have side 8 cm. Find total perimeter of both.","options":{"A":"72 cm","B":"84 cm","C":"96 cm","D":"108 cm"},"correct_answer":"C"},
    {"id":141,"difficulty":"hard","question":"A congruent pair of rectangles have area 120 cm². If length is 15 cm, find width.","options":{"A":"6 cm","B":"8 cm","C":"10 cm","D":"12 cm"},"correct_answer":"A"},
    {"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":"B"},
    {"id":143,"difficulty":"hard","question":"In parallelogram ABCD ≅ parallelogram WXYZ, AB = 12 cm, BC = 9 cm. Find perimeter.","options":{"A":"36 cm","B":"42 cm","C":"48 cm","D":"54 cm"},"correct_answer":"C"},
    {"id":144,"difficulty":"hard","question":"Two congruent squares have combined area 128 cm². Find side of one square.","options":{"A":"6 cm","B":"8 cm","C":"10 cm","D":"12 cm"},"correct_answer":"B"},
    {"id":145,"difficulty":"hard","question":"Congruent triangles have sides in ratio 3:4:5 with perimeter 48 cm. Find largest side.","options":{"A":"12 cm","B":"16 cm","C":"20 cm","D":"24 cm"},"correct_answer":"C"},
    {"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":"C"},
    {"id":147,"difficulty":"hard","question":"In ΔABC ≅ ΔPQR, AC = (5x−4) cm and PR = 31 cm. Find x.","options":{"A":"5","B":"6","C":"7","D":"8"},"correct_answer":"C"},
    {"id":148,"difficulty":"hard","question":"Two congruent rhombuses have side 13 cm and one diagonal 10 cm. Find other diagonal.","options":{"A":"18 cm","B":"20 cm","C":"24 cm","D":"26 cm"},"correct_answer":"C"},
    {"id":149,"difficulty":"hard","question":"Two congruent regular pentagons have side 9 cm. Find total perimeter of both.","options":{"A":"72 cm","B":"81 cm","C":"90 cm","D":"99 cm"},"correct_answer":"C"},
    {"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":"A"}
]
}