{
  "title": "Applications of Congruence - Grade 7 CBSE",
  "total_questions": 150,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "If two triangles are congruent, their corresponding angles are:", "options": {"A": "Equal", "B": "Complementary", "C": "Supplementary", "D": "Different"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "Two congruent figures have:", "options": {"A": "Same shape only", "B": "Same size only", "C": "Same shape and size", "D": "Different shape and size"}, "correct_answer": "C"},
    {"id": 3, "difficulty": "easy", "question": "If ΔABC ≅ ΔDEF, then side AB corresponds to:", "options": {"A": "DE", "B": "EF", "C": "FD", "D": "BC"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "Which congruence criterion would you use if two sides and included angle of one triangle equal two sides and included angle of another?", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "If two squares have equal sides, they are:", "options": {"A": "Similar", "B": "Congruent", "C": "Different", "D": "Parallel"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "In congruent triangles, corresponding sides are:", "options": {"A": "Equal", "B": "Proportional", "C": "Parallel", "D": "Perpendicular"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "If ΔPQR ≅ ΔXYZ, then ∠P corresponds to:", "options": {"A": "∠X", "B": "∠Y", "C": "∠Z", "D": "∠Q"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "Two circles with equal radii are:", "options": {"A": "Similar", "B": "Congruent", "C": "Different", "D": "Concentric"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "Which symbol is used to represent congruence?", "options": {"A": "≈", "B": "≅", "C": "∼", "D": "="}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "If two rectangles have equal length and width, they are:", "options": {"A": "Similar", "B": "Congruent", "C": "Different", "D": "Parallel"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "Congruent figures can be made to coincide by:", "options": {"A": "Rotation", "B": "Reflection", "C": "Translation", "D": "All of these"}, "correct_answer": "D"},
    {"id": 12, "difficulty": "easy", "question": "If ΔABC ≅ ΔDEF, then BC corresponds to:", "options": {"A": "DE", "B": "EF", "C": "FD", "D": "DF"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "Two triangles are congruent if they have:", "options": {"A": "Same area", "B": "Same perimeter", "C": "Same shape and size", "D": "Same angles"}, "correct_answer": "C"},
    {"id": 14, "difficulty": "easy", "question": "In real life, congruence is used in:", "options": {"A": "Manufacturing identical parts", "B": "Architecture", "C": "Pattern making", "D": "All of these"}, "correct_answer": "D"},
    {"id": 15, "difficulty": "easy", "question": "If two line segments have equal length, they are:", "options": {"A": "Parallel", "B": "Congruent", "C": "Perpendicular", "D": "Equal"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "Which congruence criterion requires right angle, hypotenuse, and one side?", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS"}, "correct_answer": "D"},
    {"id": 17, "difficulty": "easy", "question": "If two angles have equal measure, they are:", "options": {"A": "Complementary", "B": "Congruent", "C": "Supplementary", "D": "Adjacent"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "Congruent triangles have:", "options": {"A": "Equal area", "B": "Equal perimeter", "C": "Both A and B", "D": "Neither A nor B"}, "correct_answer": "C"},
    {"id": 19, "difficulty": "easy", "question": "Which is NOT a congruence criterion for triangles?", "options": {"A": "SSS", "B": "SAS", "C": "AAA", "D": "ASA"}, "correct_answer": "C"},
    {"id": 20, "difficulty": "easy", "question": "In congruent polygons, corresponding vertices match in:", "options": {"A": "Order", "B": "Position", "C": "Both A and B", "D": "Neither A nor B"}, "correct_answer": "C"},
    
    {"id": 21, "difficulty": "medium", "question": "In quadrilateral ABCD ≅ quadrilateral PQRS, if AB = 5 cm, what is PQ?", "options": {"A": "3 cm", "B": "4 cm", "C": "5 cm", "D": "6 cm"}, "correct_answer": "C"},
    {"id": 22, "difficulty": "medium", "question": "If ΔABC ≅ ΔPQR and AB = 7 cm, BC = 5 cm, AC = 6 cm, what is the perimeter of ΔPQR?", "options": {"A": "15 cm", "B": "16 cm", "C": "17 cm", "D": "18 cm"}, "correct_answer": "D"},
    {"id": 23, "difficulty": "medium", "question": "Two triangles are congruent by SAS criterion. If included angle is 60°, what is measure of corresponding angle in other triangle?", "options": {"A": "30°", "B": "60°", "C": "90°", "D": "120°"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "In ΔABC ≅ ΔDEF, if ∠A = 45° and ∠B = 75°, what is ∠E?", "options": {"A": "45°", "B": "60°", "C": "75°", "D": "90°"}, "correct_answer": "C"},
    {"id": 25, "difficulty": "medium", "question": "A rectangular photo frame measures 15 cm × 10 cm. Another frame is congruent to it. What could be its dimensions?", "options": {"A": "10 cm × 15 cm", "B": "15 cm × 10 cm", "C": "20 cm × 10 cm", "D": "15 cm × 12 cm"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "If two right triangles have hypotenuse of 13 cm and one side of 5 cm each, which congruence criterion applies?", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS"}, "correct_answer": "D"},
    {"id": 27, "difficulty": "medium", "question": "In trapezoid ABCD ≅ trapezoid PQRS, if AB corresponds to PQ and AB = 8 cm, what is PQ?", "options": {"A": "4 cm", "B": "6 cm", "C": "8 cm", "D": "10 cm"}, "correct_answer": "C"},
    {"id": 28, "difficulty": "medium", "question": "Two congruent triangles have areas of 24 cm² each. If one triangle has base 8 cm, what is its height?", "options": {"A": "3 cm", "B": "6 cm", "C": "8 cm", "D": "12 cm"}, "correct_answer": "B"},
    {"id": 29, "difficulty": "medium", "question": "If ΔXYZ ≅ ΔLMN and perimeter of ΔXYZ is 30 cm, what is perimeter of ΔLMN?", "options": {"A": "15 cm", "B": "20 cm", "C": "30 cm", "D": "45 cm"}, "correct_answer": "C"},
    {"id": 30, "difficulty": "medium", "question": "In parallelogram ABCD ≅ parallelogram WXYZ, if ∠A = 110°, what is ∠W?", "options": {"A": "70°", "B": "90°", "C": "110°", "D": "130°"}, "correct_answer": "C"},
    {"id": 31, "difficulty": "medium", "question": "Two triangles are congruent by ASA. If two angles are 40° and 60°, what is third angle in both triangles?", "options": {"A": "60°", "B": "70°", "C": "80°", "D": "90°"}, "correct_answer": "C"},
    {"id": 32, "difficulty": "medium", "question": "If square A has side 7 cm and square B is congruent to it, what is area of square B?", "options": {"A": "14 cm²", "B": "28 cm²", "C": "49 cm²", "D": "56 cm²"}, "correct_answer": "C"},
    {"id": 33, "difficulty": "medium", "question": "In ΔABC ≅ ΔPQR, AB = 3x+2 and PQ = 14. What is value of x?", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "C"},
    {"id": 34, "difficulty": "medium", "question": "Two congruent isosceles triangles have equal base angles of 55° each. What is vertex angle?", "options": {"A": "60°", "B": "70°", "C": "80°", "D": "90°"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "If two circles are congruent and one has radius 5 cm, what is diameter of other circle?", "options": {"A": "5 cm", "B": "10 cm", "C": "15 cm", "D": "20 cm"}, "correct_answer": "B"},
    {"id": 36, "difficulty": "medium", "question": "In rhombus ABCD ≅ rhombus PQRS, if diagonal AC = 10 cm, what is PR?", "options": {"A": "5 cm", "B": "10 cm", "C": "15 cm", "D": "20 cm"}, "correct_answer": "B"},
    {"id": 37, "difficulty": "medium", "question": "Two triangles congruent by SSS have sides 6 cm, 8 cm, 10 cm. What type of triangles are they?", "options": {"A": "Acute", "B": "Obtuse", "C": "Right", "D": "Equilateral"}, "correct_answer": "C"},
    {"id": 38, "difficulty": "medium", "question": "If regular hexagon A ≅ regular hexagon B, and side of A is 4 cm, what is perimeter of B?", "options": {"A": "16 cm", "B": "20 cm", "C": "24 cm", "D": "28 cm"}, "correct_answer": "C"},
    {"id": 39, "difficulty": "medium", "question": "In ΔABC ≅ ΔDEF, if AB = 2x-3 and DE = 9, find x.", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "D"},
    {"id": 40, "difficulty": "medium", "question": "Two congruent rectangles have length:width ratio 3:2. If length is 12 cm, what is width?", "options": {"A": "4 cm", "B": "6 cm", "C": "8 cm", "D": "10 cm"}, "correct_answer": "C"},
    {"id": 41, "difficulty": "medium", "question": "If ΔPQR ≅ ΔSTU and ∠P = 50°, ∠Q = 70°, what is ∠U?", "options": {"A": "50°", "B": "60°", "C": "70°", "D": "80°"}, "correct_answer": "B"},
    {"id": 42, "difficulty": "medium", "question": "In kite ABCD ≅ kite PQRS, if diagonal AC = 16 cm, what is diagonal PR?", "options": {"A": "8 cm", "B": "12 cm", "C": "16 cm", "D": "20 cm"}, "correct_answer": "C"},
    {"id": 43, "difficulty": "medium", "question": "Two congruent triangles have base 10 cm and height 6 cm. What is area of each?", "options": {"A": "15 cm²", "B": "30 cm²", "C": "60 cm²", "D": "120 cm²"}, "correct_answer": "B"},
   {"id": 44, "difficulty": "medium", "question": "If regular pentagon A ≅ regular pentagon B, and interior angle of A is 108°, what is interior angle of B?", "options": {"A": "72°", "B": "90°", "C": "108°", "D": "120°"}, "correct_answer": "C"}, {"id": 45, "difficulty": "medium", "question": "In ΔABC ≅ ΔXYZ, if BC = y+4 and YZ = 12, find y.", "options": {"A": "6", "B": "7", "C": "8", "D": "9"}, "correct_answer": "C"},
    {"id": 46, "difficulty": "medium", "question": "Two congruent circles have circumference 44 cm. What is radius? (π=22/7)", "options": {"A": "3.5 cm", "B": "7 cm", "C": "10.5 cm", "D": "14 cm"}, "correct_answer": "B"},
    {"id": 47, "difficulty": "medium", "question": "If parallelogram ABCD ≅ parallelogram EFGH, and AB = 15 cm, what is EF?", "options": {"A": "10 cm", "B": "15 cm", "C": "20 cm", "D": "25 cm"}, "correct_answer": "B"},
    {"id": 48, "difficulty": "medium", "question": "Two triangles are congruent by ASA with angles 35° and 65°. What is third angle?", "options": {"A": "70°", "B": "75°", "C": "80°", "D": "85°"}, "correct_answer": "C"},
    {"id": 49, "difficulty": "medium", "question": "In trapezium ABCD ≅ trapezium PQRS, if AD corresponds to PS and AD = 9 cm, what is PS?", "options": {"A": "4.5 cm", "B": "9 cm", "C": "12 cm", "D": "18 cm"}, "correct_answer": "B"},
    {"id": 50, "difficulty": "medium", "question": "If two equilateral triangles are congruent and side is 8 cm, what is height? (√3≈1.73)", "options": {"A": "4 cm", "B": "5.2 cm", "C": "6.4 cm", "D": "6.93 cm"}, "correct_answer": "D"},
    {"id": 51, "difficulty": "medium", "question": "In ΔABC ≅ ΔPQR, if ∠B = 3x+10 and ∠Q = 70°, find x.", "options": {"A": "15", "B": "20", "C": "25", "D": "30"}, "correct_answer": "B"},
    {"id": 52, "difficulty": "medium", "question": "Two congruent squares have diagonal 10√2 cm. What is side length?", "options": {"A": "5 cm", "B": "8 cm", "C": "10 cm", "D": "12 cm"}, "correct_answer": "C"},
    {"id": 53, "difficulty": "medium", "question": "If ΔXYZ ≅ ΔLMN and perimeter is 45 cm with sides in ratio 2:3:4, what is longest side?", "options": {"A": "10 cm", "B": "15 cm", "C": "20 cm", "D": "25 cm"}, "correct_answer": "C"},
    {"id": 54, "difficulty": "medium", "question": "In rhombus ABCD ≅ rhombus PQRS, if ∠A = 120°, what is ∠P?", "options": {"A": "60°", "B": "90°", "C": "120°", "D": "150°"}, "correct_answer": "C"},
    {"id": 55, "difficulty": "medium", "question": "Two congruent right triangles have legs 6 cm and 8 cm. What is hypotenuse?", "options": {"A": "9 cm", "B": "10 cm", "C": "12 cm", "D": "14 cm"}, "correct_answer": "B"},
    {"id": 56, "difficulty": "medium", "question": "If regular octagon A ≅ regular octagon B, and side is 5 cm, what is perimeter of B?", "options": {"A": "20 cm", "B": "30 cm", "C": "40 cm", "D": "50 cm"}, "correct_answer": "C"},
    {"id": 57, "difficulty": "medium", "question": "In ΔABC ≅ ΔDEF, if AC = 4x-6 and DF = 18, find x.", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "C"},
    {"id": 58, "difficulty": "medium", "question": "Two congruent isosceles triangles have equal sides 13 cm and base 10 cm. What is height?", "options": {"A": "5 cm", "B": "10 cm", "C": "12 cm", "D": "15 cm"}, "correct_answer": "C"},
    {"id": 59, "difficulty": "medium", "question": "If circle A ≅ circle B and area is 154 cm² (π=22/7), what is radius?", "options": {"A": "5 cm", "B": "6 cm", "C": "7 cm", "D": "8 cm"}, "correct_answer": "C"},
    {"id": 60, "difficulty": "medium", "question": "In parallelogram ABCD ≅ parallelogram WXYZ, if AB = 2y+3 and WX = 13, find y.", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "C"},
    {"id": 61, "difficulty": "medium", "question": "Two congruent triangles have sides 7 cm, 24 cm, 25 cm. What type of triangle?", "options": {"A": "Acute", "B": "Right", "C": "Obtuse", "D": "Equilateral"}, "correct_answer": "B"},
    {"id": 62, "difficulty": "medium", "question": "If ΔPQR ≅ ΔSTU and ∠R = 55°, ∠S = 65°, what is ∠T?", "options": {"A": "50°", "B": "55°", "C": "60°", "D": "65°"}, "correct_answer": "C"},
    {"id": 63, "difficulty": "medium", "question": "In kite ABCD ≅ kite PQRS, if AB = 15 cm, what is PQ?", "options": {"A": "10 cm", "B": "12 cm", "C": "15 cm", "D": "18 cm"}, "correct_answer": "C"},
    {"id": 64, "difficulty": "medium", "question": "Two congruent rectangles have perimeter 40 cm. If length is 12 cm, what is width?", "options": {"A": "4 cm", "B": "6 cm", "C": "8 cm", "D": "10 cm"}, "correct_answer": "C"},
    {"id": 65, "difficulty": "medium", "question": "If regular hexagon A ≅ regular hexagon B, and apothem is 5√3 cm, what is side?", "options": {"A": "5 cm", "B": "8 cm", "C": "10 cm", "D": "12 cm"}, "correct_answer": "C"},
    {"id": 66, "difficulty": "medium", "question": "In ΔABC ≅ ΔXYZ, if BC = 3z-2 and YZ = 16, find z.", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "C"},
    {"id": 67, "difficulty": "medium", "question": "Two congruent equilateral triangles have height 6√3 cm. What is side?", "options": {"A": "6 cm", "B": "8 cm", "C": "10 cm", "D": "12 cm"}, "correct_answer": "D"},
    {"id": 68, "difficulty": "medium", "question": "If circle A ≅ circle B and circumference is 66 cm (π=22/7), what is diameter?", "options": {"A": "14 cm", "B": "21 cm", "C": "28 cm", "D": "35 cm"}, "correct_answer": "B"},
    {"id": 69, "difficulty": "medium", "question": "In rhombus ABCD ≅ rhombus PQRS, if AC = 24 cm, what is PR?", "options": {"A": "12 cm", "B": "18 cm", "C": "24 cm", "D": "30 cm"}, "correct_answer": "C"},
    {"id": 70, "difficulty": "medium", "question": "Two congruent isosceles triangles have base angles 40° each. What is vertex angle?", "options": {"A": "80°", "B": "90°", "C": "100°", "D": "110°"}, "correct_answer": "C"},
    {"id": 71, "difficulty": "medium", "question": "If ΔXYZ ≅ ΔLMN and sides are x, x+2, x+4 with perimeter 36 cm, find longest side.", "options": {"A": "10 cm", "B": "12 cm", "C": "14 cm", "D": "16 cm"}, "correct_answer": "C"},
    {"id": 72, "difficulty": "medium", "question": "In trapezoid ABCD ≅ trapezoid PQRS, if BC corresponds to QR and BC = 11 cm, what is QR?", "options": {"A": "5.5 cm", "B": "11 cm", "C": "16.5 cm", "D": "22 cm"}, "correct_answer": "B"},
    {"id": 73, "difficulty": "medium", "question": "Two congruent squares have area 81 cm². What is perimeter?", "options": {"A": "18 cm", "B": "27 cm", "C": "36 cm", "D": "45 cm"}, "correct_answer": "C"},
    {"id": 74, "difficulty": "medium", "question": "If parallelogram ABCD ≅ parallelogram EFGH, and ∠A = 75°, what is ∠E?", "options": {"A": "65°", "B": "75°", "C": "85°", "D": "105°"}, "correct_answer": "B"},
    {"id": 75, "difficulty": "medium", "question": "In ΔABC ≅ ΔPQR, if ∠A = 2x+10 and ∠P = 50°, find x.", "options": {"A": "15", "B": "20", "C": "25", "D": "30"}, "correct_answer": "B"},
    {"id": 76, "difficulty": "medium", "question": "Two congruent right triangles have area 30 cm². If one leg is 6 cm, what is other leg?", "options": {"A": "5 cm", "B": "8 cm", "C": "10 cm", "D": "12 cm"}, "correct_answer": "C"},
    {"id": 77, "difficulty": "medium", "question": "If regular pentagon A ≅ regular pentagon B, and side is 8 cm, what is perimeter?", "options": {"A": "24 cm", "B": "32 cm", "C": "40 cm", "D": "48 cm"}, "correct_answer": "C"},
    {"id": 78, "difficulty": "medium", "question": "In kite ABCD ≅ kite PQRS, if diagonal BD = 20 cm, what is QS?", "options": {"A": "10 cm", "B": "15 cm", "C": "20 cm", "D": "25 cm"}, "correct_answer": "C"},
    {"id": 79, "difficulty": "medium", "question": "Two congruent equilateral triangles have perimeter 45 cm. What is side?", "options": {"A": "10 cm", "B": "12 cm", "C": "15 cm", "D": "18 cm"}, "correct_answer": "C"},
    {"id": 80, "difficulty": "medium", "question": "If circle A ≅ circle B and radius is 10.5 cm, what is area? (π=22/7)", "options": {"A": "154 cm²", "B": "308 cm²", "C": "346.5 cm²", "D": "693 cm²"}, "correct_answer": "C"},
    
    {"id": 81, "difficulty": "hard", "question": "In ΔABC ≅ ΔPQR, AB = (3x-4) cm, PQ = (x+8) cm. If perimeter of ΔABC is 48 cm and BC:CA = 3:4, find length of QR.", "options": {"A": "12 cm", "B": "14 cm", "C": "16 cm", "D": "18 cm"}, "correct_answer": "C"},
    {"id": 82, "difficulty": "hard", "question": "Two congruent trapezoids have parallel sides 10 cm and 16 cm with height 6 cm. Non-parallel sides are equal. If one non-parallel side is 5 cm, what is area?", "options": {"A": "52 cm²", "B": "65 cm²", "C": "78 cm²", "D": "84 cm²"}, "correct_answer": "C"},
    {"id": 83, "difficulty": "hard", "question": "ΔABC ≅ ΔDEF. ∠A = (2x+15)°, ∠D = 55°, ∠B = (3x-10)°, ∠E = (x+20)°. Find ∠C.", "options": {"A": "45°", "B": "55°", "C": "65°", "D": "75°"}, "correct_answer": "D"},
    {"id": 84, "difficulty": "hard", "question": "Two congruent regular polygons have interior angle 150° each. How many sides do they have?", "options": {"A": "10", "B": "12", "C": "15", "D": "18"}, "correct_answer": "B"},
    {"id": 85, "difficulty": "hard", "question": "In rhombus ABCD ≅ rhombus PQRS, diagonals AC = 16 cm, BD = 12 cm. What is side length of rhombus?", "options": {"A": "8 cm", "B": "9 cm", "C": "10 cm", "D": "12 cm"}, "correct_answer": "C"},
    {"id": 86, "difficulty": "hard", "question": "ΔPQR ≅ ΔXYZ. PQ = (2a+3) cm, XY = 13 cm, QR = (3b-2) cm, YZ = 16 cm, PR = (c+7) cm, XZ = 15 cm. Find a+b+c.", "options": {"A": "18", "B": "21", "C": "24", "D": "27"}, "correct_answer": "C"},
    {"id": 87, "difficulty": "hard", "question": "Two congruent circles intersect. Distance between centers is 12 cm. If radius of each circle is 10 cm, what is length of common chord?", "options": {"A": "12 cm", "B": "14 cm", "C": "16 cm", "D": "18 cm"}, "correct_answer": "C"},
    {"id": 88, "difficulty": "hard", "question": "In ΔABC ≅ ΔLMN, AB = 2x+3, LM = 17, BC = 3y-4, MN = 20, AC = z+8, LN = 21. Find x+y+z.", "options": {"A": "30", "B": "33", "C": "36", "D": "39"}, "correct_answer": "B"},
    {"id": 89, "difficulty": "hard", "question": "Two congruent isosceles triangles have perimeter 50 cm. Equal sides are 5 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": 90, "difficulty": "hard", "question": "Regular hexagon A ≅ regular hexagon B. Distance between parallel sides is 10√3 cm. Find area of each hexagon.", "options": {"A": "150√3 cm²", "B": "200√3 cm²", "C": "250√3 cm²", "D": "300√3 cm²"}, "correct_answer": "D"},
    {"id": 91, "difficulty": "hard", "question": "In parallelogram ABCD ≅ parallelogram WXYZ, AB = 3x-2, WX = 16, AD = 2y+4, WZ = 18, ∠A = (z+20)°, ∠W = 70°. Find x+y+z.", "options": {"A": "40", "B": "45", "C": "50", "D": "55"}, "correct_answer": "C"},
    {"id": 92, "difficulty": "hard", "question": "Two congruent right circular cones have slant height 13 cm and radius 5 cm. Find height.", "options": {"A": "8 cm", "B": "10 cm", "C": "12 cm", "D": "15 cm"}, "correct_answer": "C"},
    {"id": 93, "difficulty": "hard", "question": "ΔABC ≅ ΔDEF. AB = (p+3) cm, DE = 12 cm, BC = (2q-1) cm, EF = 15 cm, ∠B = (3r+10)°, ∠E = 70°. Find p+q+r.", "options": {"A": "20", "B": "23", "C": "26", "D": "29"}, "correct_answer": "C"},
    {"id": 94, "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": 95, "difficulty": "hard", "question": "In kite ABCD ≅ kite PQRS, AC = 24 cm, BD = 10 cm, AB = AD = 13 cm. Find area of kite.", "options": {"A": "60 cm²", "B": "120 cm²", "C": "130 cm²", "D": "156 cm²"}, "correct_answer": "B"},
    {"id": 96, "difficulty": "hard", "question": "Two congruent regular polygons have exterior angle 24°. How many diagonals does each have?", "options": {"A": "35", "B": "44", "C": "54", "D": "65"}, "correct_answer": "C"},
    {"id": 97, "difficulty": "hard", "question": "ΔPQR ≅ ΔSTU. PQ = 3x-4, ST = 17, QR = 2y+5, TU = 19, ∠Q = 4z+5, ∠T = 65°. Find x+y+z.", "options": {"A": "24", "B": "27", "C": "30", "D": "33"}, "correct_answer": "B"},
    {"id": 98, "difficulty": "hard", "question": "Two congruent frustums of pyramids have parallel sides 6 cm and 10 cm square, height 4 cm. If slant height is 5 cm, find total surface area.", "options": {"A": "200 cm²", "B": "240 cm²", "C": "280 cm²", "D": "320 cm²"}, "correct_answer": "B"},
    {"id": 99, "difficulty": "hard", "question": "In ΔABC ≅ ΔXYZ, AB = 2a+5, XY = 21, BC = 3b-7, YZ = 26, ∠A = 4c+10, ∠X = 50°. Find a+b+c.", "options": {"A": "25", "B": "28", "C": "31", "D": "34"}, "correct_answer": "C"},
   {"id": 100, "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":101,"difficulty":"easy","question":"Two congruent triangles have one side of 6 cm. What is the length of the corresponding side in the other triangle?","options":{"A":"3 cm","B":"6 cm","C":"9 cm","D":"12 cm"},"correct_answer":"B"},
  {"id":102,"difficulty":"easy","question":"If one angle of a triangle is 40° and the triangle is congruent to another, what is the measure of the corresponding angle?","options":{"A":"20°","B":"40°","C":"60°","D":"80°"},"correct_answer":"B"},
  {"id":103,"difficulty":"easy","question":"Two congruent squares each have side 5 cm. What is the perimeter of one square?","options":{"A":"10 cm","B":"15 cm","C":"20 cm","D":"25 cm"},"correct_answer":"C"},
  {"id":104,"difficulty":"easy","question":"If two congruent rectangles have length 8 cm and width 4 cm, what is the area of each?","options":{"A":"24 cm²","B":"28 cm²","C":"32 cm²","D":"36 cm²"},"correct_answer":"C"},
  {"id":105,"difficulty":"easy","question":"Two congruent circles have radius 7 cm. What is the diameter of each circle?","options":{"A":"7 cm","B":"10 cm","C":"14 cm","D":"21 cm"},"correct_answer":"C"},
  {"id":106,"difficulty":"easy","question":"If ΔABC ≅ ΔPQR and AC = 9 cm, what is PR?","options":{"A":"4.5 cm","B":"9 cm","C":"12 cm","D":"18 cm"},"correct_answer":"B"},
  {"id":107,"difficulty":"easy","question":"Two congruent equilateral triangles each have side 6 cm. What is the perimeter of one triangle?","options":{"A":"12 cm","B":"15 cm","C":"18 cm","D":"24 cm"},"correct_answer":"C"},
  {"id":108,"difficulty":"easy","question":"If two congruent right triangles have hypotenuse 10 cm, what is the hypotenuse of the other triangle?","options":{"A":"5 cm","B":"8 cm","C":"10 cm","D":"12 cm"},"correct_answer":"C"},
  {"id":109,"difficulty":"easy","question":"Two congruent squares have diagonal 10√2 cm. What is the side of each square?","options":{"A":"5 cm","B":"7 cm","C":"10 cm","D":"14 cm"},"correct_answer":"C"},
  {"id":110,"difficulty":"easy","question":"If two congruent triangles have equal bases of 12 cm, what is the base of the other triangle?","options":{"A":"6 cm","B":"10 cm","C":"12 cm","D":"24 cm"},"correct_answer":"C"},
  {"id":111,"difficulty":"easy","question":"Two congruent rectangles have perimeter 30 cm. What is the perimeter of the other rectangle?","options":{"A":"15 cm","B":"20 cm","C":"30 cm","D":"60 cm"},"correct_answer":"C"},
  {"id":112,"difficulty":"easy","question":"If two congruent circles have circumference 44 cm, what is the circumference of the other?","options":{"A":"22 cm","B":"44 cm","C":"66 cm","D":"88 cm"},"correct_answer":"B"},
  {"id":113,"difficulty":"easy","question":"In two congruent triangles, one angle is 55°. What is the corresponding angle?","options":{"A":"35°","B":"45°","C":"55°","D":"65°"},"correct_answer":"C"},
  {"id":114,"difficulty":"easy","question":"Two congruent rhombuses have side length 6 cm. What is the side of the other rhombus?","options":{"A":"3 cm","B":"6 cm","C":"9 cm","D":"12 cm"},"correct_answer":"B"},
  {"id":115,"difficulty":"easy","question":"If two congruent trapeziums have height 5 cm, what is the height of the other trapezium?","options":{"A":"2.5 cm","B":"5 cm","C":"7.5 cm","D":"10 cm"},"correct_answer":"B"},
  {"id":116,"difficulty":"easy","question":"Two congruent triangles have area 24 cm² each. What is the area of the other triangle?","options":{"A":"12 cm²","B":"18 cm²","C":"24 cm²","D":"48 cm²"},"correct_answer":"C"},
  {"id":117,"difficulty":"easy","question":"If two congruent squares have area 64 cm², what is the side length?","options":{"A":"6 cm","B":"7 cm","C":"8 cm","D":"9 cm"},"correct_answer":"C"},
  {"id":118,"difficulty":"easy","question":"Two congruent rectangles have width 5 cm. What is the width of the other rectangle?","options":{"A":"2.5 cm","B":"5 cm","C":"10 cm","D":"15 cm"},"correct_answer":"B"},
  {"id":119,"difficulty":"easy","question":"If two congruent circles have radius 3.5 cm, what is the radius of the other circle?","options":{"A":"1.75 cm","B":"3.5 cm","C":"7 cm","D":"14 cm"},"correct_answer":"B"},
  {"id":120,"difficulty":"easy","question":"Two congruent triangles have equal corresponding angles. How many angles are equal in total?","options":{"A":"2","B":"3","C":"4","D":"6"},"correct_answer":"D"},

  {"id":121,"difficulty":"medium","question":"If ΔABC ≅ ΔPQR and AB = 2x + 6, PQ = 14, find x.","options":{"A":"3","B":"4","C":"5","D":"6"},"correct_answer":"B"},
  {"id":122,"difficulty":"medium","question":"Two congruent triangles have perimeter 42 cm. If two sides are 10 cm and 14 cm, find the third side.","options":{"A":"16 cm","B":"18 cm","C":"20 cm","D":"22 cm"},"correct_answer":"A"},
  {"id":123,"difficulty":"medium","question":"In ΔXYZ ≅ ΔLMN, if ∠X = 48° and ∠Y = 62°, find ∠N.","options":{"A":"48°","B":"62°","C":"70°","D":"90°"},"correct_answer":"C"},
  {"id":124,"difficulty":"medium","question":"Two congruent squares have diagonal 14√2 cm. What is the area of each square?","options":{"A":"98 cm²","B":"144 cm²","C":"196 cm²","D":"224 cm²"},"correct_answer":"C"},
  {"id":125,"difficulty":"medium","question":"If a rectangle congruent to another has length 12 cm and width 5 cm, what is its perimeter?","options":{"A":"24 cm","B":"30 cm","C":"34 cm","D":"40 cm"},"correct_answer":"C"},
  {"id":126,"difficulty":"medium","question":"Two congruent right triangles have legs 9 cm and 12 cm. What is the hypotenuse?","options":{"A":"13 cm","B":"14 cm","C":"15 cm","D":"16 cm"},"correct_answer":"C"},
  {"id":127,"difficulty":"medium","question":"In ΔABC ≅ ΔDEF, BC = 3y − 2 and EF = 16. Find y.","options":{"A":"5","B":"6","C":"7","D":"8"},"correct_answer":"C"},
  {"id":128,"difficulty":"medium","question":"Two congruent circles have area 154 cm² each (π = 22/7). Find the radius.","options":{"A":"5 cm","B":"6 cm","C":"7 cm","D":"8 cm"},"correct_answer":"C"},
  {"id":129,"difficulty":"medium","question":"If two congruent equilateral triangles have side 10 cm, what is their height? (√3 ≈ 1.73)","options":{"A":"6.5 cm","B":"7.5 cm","C":"8.66 cm","D":"10 cm"},"correct_answer":"C"},
  {"id":130,"difficulty":"medium","question":"Two congruent rectangles have area 96 cm² and length 12 cm. What is the width?","options":{"A":"6 cm","B":"8 cm","C":"10 cm","D":"12 cm"},"correct_answer":"B"},
{"id":131,"difficulty":"hard","question":"ΔABC ≅ ΔPQR. AB = 3x − 1, PQ = 14, BC = 4x − 5. Find the perimeter of ΔABC.","options":{"A":"36 cm","B":"39 cm","C":"42 cm","D":"45 cm"},"correct_answer":"C"},
  {"id":132,"difficulty":"hard","question":"Two congruent isosceles triangles have equal sides 13 cm and base 10 cm. Find area if height is 12 cm.","options":{"A":"48 cm²","B":"60 cm²","C":"72 cm²","D":"84 cm²"},"correct_answer":"C"},
  {"id":133,"difficulty":"hard","question":"In ΔXYZ ≅ ΔLMN, XY = 2a+3, LM = 15, YZ = 3a−2. Find the value of a.","options":{"A":"4","B":"5","C":"6","D":"7"},"correct_answer":"B"},
  {"id":134,"difficulty":"hard","question":"Two congruent rhombuses have diagonals 16 cm and 12 cm. Find the area of one rhombus.","options":{"A":"72 cm²","B":"84 cm²","C":"96 cm²","D":"108 cm²"},"correct_answer":"C"},
  {"id":135,"difficulty":"hard","question":"Two congruent circles intersect such that distance between centers is 10 cm and radius is 13 cm. Find half length of common chord.","options":{"A":"5 cm","B":"10 cm","C":"12 cm","D":"13 cm"},"correct_answer":"C"},
  {"id":136,"difficulty":"hard","question":"In ΔABC ≅ ΔDEF, angles are in ratio 2:3:4. Find the smallest angle.","options":{"A":"20°","B":"30°","C":"40°","D":"50°"},"correct_answer":"C"},
  {"id":137,"difficulty":"hard","question":"Two congruent regular hexagons have side 6 cm. Find the perimeter of each.","options":{"A":"30 cm","B":"36 cm","C":"42 cm","D":"48 cm"},"correct_answer":"B"},
  {"id":138,"difficulty":"hard","question":"ΔPQR ≅ ΔXYZ. PQ = x+5, QR = 2x−3, PR = 18. Find x.","options":{"A":"7","B":"8","C":"9","D":"10"},"correct_answer":"C"},
  {"id":139,"difficulty":"hard","question":"Two congruent right triangles have area 48 cm². If one leg is 8 cm, find the other leg.","options":{"A":"6 cm","B":"10 cm","C":"12 cm","D":"14 cm"},"correct_answer":"C"},
  {"id":140,"difficulty":"hard","question":"In congruent squares, diagonal is 10√2 cm. Find the perimeter.","options":{"A":"20 cm","B":"30 cm","C":"40 cm","D":"50 cm"},"correct_answer":"C"},
  {"id":141,"difficulty":"hard","question":"Two congruent trapeziums have parallel sides 12 cm and 20 cm with height 6 cm. Find area.","options":{"A":"84 cm²","B":"96 cm²","C":"120 cm²","D":"144 cm²"},"correct_answer":"C"},
  {"id":142,"difficulty":"hard","question":"ΔABC ≅ ΔPQR. AB = 2x, BC = 3x, CA = 4x and perimeter is 54 cm. Find x.","options":{"A":"3","B":"4","C":"5","D":"6"},"correct_answer":"C"},
  {"id":143,"difficulty":"hard","question":"Two congruent equilateral triangles have area 64√3 cm². Find side.","options":{"A":"8 cm","B":"10 cm","C":"12 cm","D":"14 cm"},"correct_answer":"C"},
  {"id":144,"difficulty":"hard","question":"In congruent circles, circumference is 88 cm (π = 22/7). Find radius.","options":{"A":"7 cm","B":"10 cm","C":"14 cm","D":"21 cm"},"correct_answer":"C"},
  {"id":145,"difficulty":"hard","question":"Two congruent kites have diagonals 10 cm and 24 cm. Find area.","options":{"A":"100 cm²","B":"120 cm²","C":"140 cm²","D":"160 cm²"},"correct_answer":"B"},
  {"id":146,"difficulty":"hard","question":"ΔXYZ ≅ ΔLMN. If ∠X = 2a+10 and ∠L = 50°, find a.","options":{"A":"15","B":"20","C":"25","D":"30"},"correct_answer":"B"},
  {"id":147,"difficulty":"hard","question":"Two congruent rectangles have diagonal 13 cm and width 5 cm. Find length.","options":{"A":"10 cm","B":"11 cm","C":"12 cm","D":"13 cm"},"correct_answer":"C"},
  {"id":148,"difficulty":"hard","question":"Two congruent spheres have volume 38808/21 cm³ (π=22/7). Find radius.","options":{"A":"5 cm","B":"7 cm","C":"14 cm","D":"21 cm"},"correct_answer":"B"}, {"id":149,"difficulty":"hard","question":"ΔABC ≅ ΔPQR. AB = x+4, BC = x+6, CA = x+10 and perimeter is 48 cm. Find x.","options":{"A":"6","B":"8","C":"10","D":"12"},"correct_answer":"B"},
  {"id":150,"difficulty":"hard","question":"Two congruent regular pentagons have side 8 cm. Find total perimeter of both.","options":{"A":"40 cm","B":"80 cm","C":"100 cm","D":"160 cm"},"correct_answer":"B"}
]
}