{
  "title": "Parallelograms (Rectilinear Figures) - Grade 9 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "In a parallelogram, opposite angles are: 🔄", "options": {"A": "Complementary", "B": "Supplementary", "C": "Equal", "D": "Acute"}, "correct_answer": "C"},
    {"id": 2, "difficulty": "easy", "question": "Which quadrilateral has both pairs of opposite sides parallel? 📐", "options": {"A": "Trapezium", "B": "Kite", "C": "Parallelogram", "D": "Cyclic quadrilateral"}, "correct_answer": "C"},
    {"id": 3, "difficulty": "easy", "question": "What is the sum of adjacent angles in a parallelogram? ➕", "options": {"A": "90°", "B": "180°", "C": "270°", "D": "360°"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "The diagonals of a parallelogram: ✖️", "options": {"A": "Are equal", "B": "Bisect each other", "C": "Are perpendicular", "D": "None of these"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "Which is NOT a property of parallelogram? 🚫", "options": {"A": "Opposite sides equal", "B": "Opposite angles equal", "C": "Diagonals equal", "D": "Diagonals bisect each other"}, "correct_answer": "C"},
    {"id": 6, "difficulty": "easy", "question": "If one angle of parallelogram is 75°, what is its adjacent angle? 📏", "options": {"A": "75°", "B": "105°", "C": "90°", "D": "15°"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "A rectangle is a special type of: 🔲", "options": {"A": "Rhombus", "B": "Parallelogram", "C": "Trapezium", "D": "Kite"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "In parallelogram ABCD, if AB = 8 cm, then CD = ? 📐", "options": {"A": "4 cm", "B": "8 cm", "C": "12 cm", "D": "16 cm"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "The diagonals of a parallelogram divide it into how many congruent triangles? 🔺", "options": {"A": "2", "B": "4", "C": "6", "D": "8"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "If one diagonal of parallelogram is 10 cm, the other diagonal: ⚖️", "options": {"A": "Must be 10 cm", "B": "May be different", "C": "Is half", "D": "Is double"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "A parallelogram with all sides equal is called: 💎", "options": {"A": "Rectangle", "B": "Rhombus", "C": "Square", "D": "Trapezium"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "In parallelogram, consecutive angles are: ↔️", "options": {"A": "Equal", "B": "Complementary", "C": "Supplementary", "D": "Right angles"}, "correct_answer": "C"},
    {"id": 13, "difficulty": "easy", "question": "Which statement is always true for parallelogram? ✅", "options": {"A": "All angles equal", "B": "Diagonals perpendicular", "C": "Opposite sides parallel", "D": "All sides equal"}, "correct_answer": "C"},
    {"id": 14, "difficulty": "easy", "question": "If base of parallelogram is 12 cm and height 5 cm, area = ? 📊", "options": {"A": "30 cm²", "B": "60 cm²", "C": "90 cm²", "D": "120 cm²"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "A square is a parallelogram with: ⬛", "options": {"A": "Equal diagonals", "B": "All angles 90°", "C": "All sides equal", "D": "All of these"}, "correct_answer": "D"},
    {"id": 16, "difficulty": "easy", "question": "In parallelogram, if one angle is right angle, then all angles are: 📐", "options": {"A": "Acute", "B": "Right", "C": "Obtuse", "D": "Equal"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "Midpoints of sides of any quadrilateral form a: 🔶", "options": {"A": "Square", "B": "Rectangle", "C": "Parallelogram", "D": "Rhombus"}, "correct_answer": "C"},
    {"id": 18, "difficulty": "easy", "question": "The diagonals of rhombus are: ✖️", "options": {"A": "Equal", "B": "Bisect at right angles", "C": "Parallel", "D": "None"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "If both pairs of opposite sides are equal, figure is: 🔳", "options": {"A": "Parallelogram", "B": "Trapezium", "C": "Kite", "D": "Cyclic"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "Parallelogram with equal diagonals is: ⚖️", "options": {"A": "Rhombus", "B": "Rectangle", "C": "Square", "D": "Both B and C"}, "correct_answer": "D"},
    {"id": 21, "difficulty": "medium", "question": "In parallelogram ABCD, ∠A = (2x+15)° and ∠B = (3x-25)°. Find ∠C. 📐", "options": {"A": "65°", "B": "85°", "C": "95°", "D": "115°"}, "correct_answer": "C"},
    {"id": 22, "difficulty": "medium", "question": "Diagonals of parallelogram are 16 cm and 20 cm. They intersect at angle 60°. Find sides if they are in ratio 3:4. ⚖️", "options": {"A": "6 cm, 8 cm", "B": "9 cm, 12 cm", "C": "12 cm, 16 cm", "D": "15 cm, 20 cm"}, "correct_answer": "B"},
    {"id": 23, "difficulty": "medium", "question": "If parallelogram has sides 12 cm and 9 cm, and one diagonal is 15 cm, find length of other diagonal. 🔄", "options": {"A": "12 cm", "B": "13 cm", "C": "14 cm", "D": "16 cm"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "In rhombus, diagonals are 24 cm and 10 cm. Find perimeter. 💎", "options": {"A": "52 cm", "B": "56 cm", "C": "60 cm", "D": "64 cm"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "ABCD is parallelogram. E is midpoint of AB, F is midpoint of CD. What type is EBFD? 🔶", "options": {"A": "Square", "B": "Rectangle", "C": "Parallelogram", "D": "Trapezium"}, "correct_answer": "C"},
    {"id": 26, "difficulty": "medium", "question": "If area of parallelogram is 72 cm² and base is 12 cm, find height. 📏", "options": {"A": "5 cm", "B": "6 cm", "C": "7 cm", "D": "8 cm"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "In parallelogram, ratio of adjacent sides is 5:7, perimeter is 48 cm. Find sides. 📐", "options": {"A": "10, 14", "B": "12, 16", "C": "15, 21", "D": "20, 28"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "Two adjacent angles of parallelogram differ by 40°. Find smaller angle. 🔄", "options": {"A": "60°", "B": "70°", "C": "80°", "D": "90°"}, "correct_answer": "B"},
    {"id": 29, "difficulty": "medium", "question": "From parallelogram ABCD, line from A meets DC at E such that DE=EC. What is AE? 🔺", "options": {"A": "Angle bisector", "B": "Median", "C": "Diagonal", "D": "Altitude"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "If diagonals of parallelogram are perpendicular, it is a: ⬛", "options": {"A": "Rectangle", "B": "Rhombus", "C": "Square", "D": "Both B and C"}, "correct_answer": "D"},
    {"id": 31, "difficulty": "medium", "question": "Parallelogram with vertices (0,0), (5,0), (6,3), (1,3). Find area. 📊", "options": {"A": "12", "B": "15", "C": "18", "D": "20"}, "correct_answer": "B"},
    {"id": 32, "difficulty": "medium", "question": "In parallelogram ABCD, AE ⟂ DC, AF ⟂ BC. If AB=10, AE=6, AD=8, find AF. 📏", "options": {"A": "4.8", "B": "5", "C": "6", "D": "7.5"}, "correct_answer": "D"},
    {"id": 33, "difficulty": "medium", "question": "If one angle of parallelogram is four times its adjacent angle, find angles. 🔢", "options": {"A": "36°,144°", "B": "45°,135°", "C": "60°,120°", "D": "72°,108°"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "Point P inside parallelogram ABCD satisfies area(APB)+area(CPD) = ? 📊", "options": {"A": "area(ABCD)", "B": "½ area(ABCD)", "C": "¼ area(ABCD)", "D": "⅓ area(ABCD)"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "Parallelogram with sides 13 and 15, one diagonal 14. Find other diagonal. ⚖️", "options": {"A": "16", "B": "18", "C": "20", "D": "22"}, "correct_answer": "C"},
    {"id": 36, "difficulty": "medium", "question": "Ratio of diagonals of rhombus is 3:4, area 96 cm². Find side. 💎", "options": {"A": "8 cm", "B": "10 cm", "C": "12 cm", "D": "14 cm"}, "correct_answer": "B"},
    {"id": 37, "difficulty": "medium", "question": "In parallelogram, sum of squares of sides equals sum of squares of diagonals? 🤔", "options": {"A": "True", "B": "False", "C": "Only for rectangle", "D": "Only for rhombus"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "If midpoints of adjacent sides of parallelogram joined, shape formed is: 🔺", "options": {"A": "Parallelogram", "B": "Rectangle", "C": "Rhombus", "D": "Square"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "Diagonals of parallelogram ABCD intersect at O. If AO=3x-1, OC=x+5, find AC. ✖️", "options": {"A": "12", "B": "16", "C": "20", "D": "24"}, "correct_answer": "B"},
    {"id": 40, "difficulty": "medium", "question": "Height corresponding to side 20 cm of parallelogram is 6 cm. If other side is 15 cm, find second height. 📏", "options": {"A": "7 cm", "B": "8 cm", "C": "9 cm", "D": "10 cm"}, "correct_answer": "B"},
    {"id": 41, "difficulty": "hard", "question": "In parallelogram ABCD, ∠A=60°, AB=10, AD=6. Find length of diagonal BD. 📐", "options": {"A": "√76", "B": "√84", "C": "√94", "D": "√104"}, "correct_answer": "C"},
    {"id": 42, "difficulty": "hard", "question": "Parallelogram and rectangle have same perimeter: 40 cm. Sides of parallelogram are 12 and 8 cm. Find ratio of areas if height of parallelogram to smaller side is 5 cm. 📊", "options": {"A": "5:6", "B": "4:5", "C": "3:4", "D": "2:3"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "hard", "question": "If diagonals of quadrilateral divide each other proportionally, it is: 🔄", "options": {"A": "Parallelogram", "B": "Trapezium", "C": "Kite", "D": "Cyclic"}, "correct_answer": "B"},
    {"id": 44, "difficulty": "hard", "question": "In parallelogram ABCD, bisectors of ∠A and ∠B meet at P on CD. Find AD if AB=20 cm. 🔺", "options": {"A": "10", "B": "15", "C": "20", "D": "25"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "hard", "question": "Rhombus with side 13 cm has one diagonal 10 cm. Find distance between opposite sides. 💎", "options": {"A": "120/13", "B": "130/13", "C": "140/13", "D": "150/13"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "hard", "question": "Ratio of areas of two parallelograms on same base and between same parallels is? 📊", "options": {"A": "1:1", "B": "1:2", "C": "2:1", "D": "Depends on shape"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "hard", "question": "ABCD is parallelogram. E on AB, F on CD such that AE=CF. Prove DE=BF. What theorem? 🧠", "options": {"A": "Opposite sides equal", "B": "SAS congruence", "C": "AAS congruence", "D": "SSS congruence"}, "correct_answer": "B"},
    {"id": 48, "difficulty": "hard", "question": "Parallelogram has vertices at (1,2), (4,3), (3,6), (0,5). Find product of lengths of diagonals. 📏", "options": {"A": "20", "B": "24", "C": "28", "D": "32"}, "correct_answer": "C"},
    {"id": 49, "difficulty": "hard", "question": "From parallelogram ABCD, line through D meets BC produced at E. If AB=8, AD=5, EC=3, find BE. 🔄", "options": {"A": "10", "B": "11", "C": "12", "D": "13"}, "correct_answer": "B"},
    {"id": 50, "difficulty": "hard", "question": "If area of rhombus is 150 cm² and one diagonal is 15 cm, find side length. 💎", "options": {"A": "√125", "B": "√136", "C": "√145", "D": "√156"}, "correct_answer": "B"},
    {"id": 51, "difficulty": "hard", "question": "In parallelogram, distances from point on diagonal to two adjacent sides are 4 and 6. Find area if side lengths 10 and 15. 📊", "options": {"A": "60", "B": "75", "C": "90", "D": "120"}, "correct_answer": "D"},
    {"id": 52, "difficulty": "hard", "question": "Parallelogram with sides a and b, diagonals d₁ and d₂ satisfy relation: ⚖️", "options": {"A": "d₁²+d₂²=2(a²+b²)", "B": "d₁²−d₂²=4ab", "C": "d₁d₂=a²+b²", "D": "d₁/d₂=a/b"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "hard", "question": "ABCD parallelogram, P on BC such that BP:PC=2:3. Line AP meets DC produced at Q. Find DQ:QC. 🔄", "options": {"A": "2:3", "B": "3:2", "C": "3:5", "D": "5:3"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "hard", "question": "In parallelogram, sum of squares of all sides equals 100. Sum of squares of diagonals is? 📐", "options": {"A": "50", "B": "100", "C": "150", "D": "200"}, "correct_answer": "B"},
    {"id": 55, "difficulty": "hard", "question": "Rhombus inscribed in rectangle of sides 16 and 30 touches midpoints. Find area of rhombus. ⬛", "options": {"A": "240", "B": "270", "C": "300", "D": "320"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "hard", "question": "Parallelogram ABCD, ∠B=120°, AB=10, AD=6. Find distance between longer sides. 📏", "options": {"A": "3√3", "B": "4√3", "C": "5√3", "D": "6√3"}, "correct_answer": "C"},
    {"id": 57, "difficulty": "hard", "question": "Point E inside parallelogram ABCD makes triangles ABE, CDE equal area. Where is E? 🎯", "options": {"A": "On diagonal AC", "B": "On diagonal BD", "C": "Midpoint of AC", "D": "Anywhere on line parallel to AB"}, "correct_answer": "B"},
    {"id": 58, "difficulty": "hard", "question": "Parallelogram with sides 8 and 12, area 48. Find acute angle between sides. 📐", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "75°"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "hard", "question": "In parallelogram, altitudes corresponding to sides 15 and 25 are 10 and h. Find h. ⛰️", "options": {"A": "6", "B": "8", "C": "9", "D": "12"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "hard", "question": "If one side of parallelogram is triple the other, and perimeter is 64, find longer side. 📏", "options": {"A": "12", "B": "16", "C": "20", "D": "24"}, "correct_answer": "D"}
  ]
}