{
  "title": "Mid-point Theorem - Grade 9 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "📐 The Mid-point Theorem applies to which shape?", "options": {"A": "Square", "B": "Triangle", "C": "Circle", "D": "Rectangle"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "🔺 In triangle ABC, D is the midpoint of AB and E is the midpoint of AC. DE is parallel to...", "options": {"A": "AB", "B": "AC", "C": "BC", "D": "AD"}, "correct_answer": "C"},
    {"id": 3, "difficulty": "easy", "question": "✅ In the same triangle, DE equals half of...", "options": {"A": "AB", "B": "AC", "C": "BC", "D": "AD"}, "correct_answer": "C"},
    {"id": 4, "difficulty": "easy", "question": "📏 The line joining the midpoints of two sides of a triangle is... to the third side.", "options": {"A": "perpendicular", "B": "parallel", "C": "equal", "D": "twice"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "🔺 In triangle ABC, if D and E are midpoints of AB and AC, then DE || BC and DE = ?", "options": {"A": "BC/2", "B": "BC", "C": "2BC", "D": "AB/2"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "✅ The converse of the Mid-point Theorem says: If a line is drawn through the midpoint of one side parallel to another side, it...", "options": {"A": "bisects the third side", "B": "is perpendicular to third side", "C": "is equal to third side", "D": "does nothing"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "📐 In triangle ABC, D is midpoint of AB. A line through D parallel to BC meets AC at E. Then E is the... of AC.", "options": {"A": "midpoint", "B": "endpoint", "C": "vertex", "D": "none"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "🔺 In quadrilateral ABCD, P, Q, R, S are midpoints of sides. The quadrilateral PQRS is a...", "options": {"A": "rectangle", "B": "parallelogram", "C": "square", "D": "trapezium"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "✅ In triangle ABC, D and E are midpoints of AB and AC. If BC=12 cm, then DE=?", "options": {"A": "6 cm", "B": "12 cm", "C": "24 cm", "D": "3 cm"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "📏 In triangle PQR, if M and N are midpoints of PQ and PR, then MN || ?", "options": {"A": "PQ", "B": "PR", "C": "QR", "D": "PM"}, "correct_answer": "C"},
    {"id": 11, "difficulty": "easy", "question": "🔺 In triangle XYZ, A and B are midpoints of XY and XZ. If YZ=20 cm, AB=?", "options": {"A": "5 cm", "B": "10 cm", "C": "20 cm", "D": "40 cm"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "✅ The Mid-point Theorem is used to prove properties of...", "options": {"A": "parallelograms", "B": "circles", "C": "polygons", "D": "all triangles"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "📐 In triangle ABC, D, E, F are midpoints of BC, CA, AB. Then triangle DEF is similar to triangle ABC with ratio...", "options": {"A": "1:1", "B": "1:2", "C": "2:1", "D": "1:3"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "🔺 In triangle ABC, if D and E are midpoints of AB and AC, then DE is called a... of the triangle.", "options": {"A": "median", "B": "midsegment", "C": "altitude", "D": "angle bisector"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "✅ The line joining midpoints of two sides of a triangle is half the length of the third side. This is...", "options": {"A": "always true", "B": "sometimes true", "C": "never true", "D": "only for right triangles"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "📏 In triangle ABC, D is midpoint of AB. DE || BC. If AE=4 cm, then EC=?", "options": {"A": "2 cm", "B": "4 cm", "C": "8 cm", "D": "12 cm"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "🔺 In triangle PQR, S and T are midpoints of PQ and PR. If ST=7 cm, QR=?", "options": {"A": "3.5 cm", "B": "7 cm", "C": "14 cm", "D": "21 cm"}, "correct_answer": "C"},
    {"id": 18, "difficulty": "easy", "question": "✅ The midpoint of a line segment divides it into... parts.", "options": {"A": "two unequal", "B": "two equal", "C": "three", "D": "four"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "📐 In triangle ABC, if D and E are midpoints, then quadrilateral DBCE is a...", "options": {"A": "trapezium", "B": "parallelogram", "C": "rectangle", "D": "square"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "🔺 In triangle ABC, D, E, F are midpoints. Then perimeter of triangle DEF is half perimeter of triangle ABC. (True/False)", "options": {"A": "True", "B": "False", "C": "Sometimes", "D": "Only if equilateral"}, "correct_answer": "A"},
    {"id": 21, "difficulty": "medium", "question": "📐 In triangle ABC, D is midpoint of AB. E is a point on AC such that DE || BC. If AD=5 cm, DB=?", "options": {"A": "2.5 cm", "B": "5 cm", "C": "10 cm", "D": "15 cm"}, "correct_answer": "B"},
    {"id": 22, "difficulty": "medium", "question": "🔺 In triangle PQR, S and T are midpoints of PQ and PR. If ∠P=50°, then ∠PST=?", "options": {"A": "50°", "B": "130°", "C": "25°", "D": "100°"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "✅ In triangle ABC, D and E are midpoints of AB and AC. If DE=8 cm, BC=?", "options": {"A": "4 cm", "B": "8 cm", "C": "16 cm", "D": "32 cm"}, "correct_answer": "C"},
    {"id": 24, "difficulty": "medium", "question": "📏 In quadrilateral ABCD, P, Q, R, S are midpoints. If AC=10 cm and BD=14 cm, then perimeter of PQRS=?", "options": {"A": "12 cm", "B": "24 cm", "C": "48 cm", "D": "20 cm"}, "correct_answer": "B"},
    {"id": 25, "difficulty": "medium", "question": "🔺 In triangle ABC, D and E are midpoints of AB and BC. F is midpoint of AC. Then DF || ?", "options": {"A": "AB", "B": "BC", "C": "AC", "D": "AE"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "✅ In triangle XYZ, A and B are midpoints of XY and YZ. If XZ=18 cm, AB=?", "options": {"A": "9 cm", "B": "18 cm", "C": "36 cm", "D": "27 cm"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "📐 In triangle PQR, M and N are midpoints of PQ and QR. O is midpoint of PR. Then quadrilateral MNOP is a...", "options": {"A": "parallelogram", "B": "rectangle", "C": "rhombus", "D": "trapezium"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "🔺 In triangle ABC, D, E, F are midpoints. Area of triangle DEF is what fraction of area of triangle ABC?", "options": {"A": "1/2", "B": "1/3", "C": "1/4", "D": "1/8"}, "correct_answer": "C"},
    {"id": 29, "difficulty": "medium", "question": "✅ In triangle ABC, D is midpoint of AB. A line through D parallel to BC meets AC at E. If AE=6 cm, EC=?", "options": {"A": "3 cm", "B": "6 cm", "C": "12 cm", "D": "18 cm"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "📏 In triangle LMN, P and Q are midpoints of LM and LN. If PQ=5x-2 and MN=3x+10, find x.", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "C"},
    {"id": 31, "difficulty": "medium", "question": "🔺 In triangle ABC, D and E are midpoints of AB and AC. If DE=4 cm and BC=3x-2, find x.", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "B"},
    {"id": 32, "difficulty": "medium", "question": "✅ In quadrilateral ABCD, midpoints of sides form parallelogram PQRS. If diagonals AC and BD are equal, then PQRS is a...", "options": {"A": "rectangle", "B": "rhombus", "C": "square", "D": "parallelogram"}, "correct_answer": "B"},
    {"id": 33, "difficulty": "medium", "question": "📐 In triangle ABC, D, E, F are midpoints. If perimeter of triangle DEF is 15 cm, perimeter of triangle ABC=?", "options": {"A": "15 cm", "B": "30 cm", "C": "45 cm", "D": "7.5 cm"}, "correct_answer": "B"},
    {"id": 34, "difficulty": "medium", "question": "🔺 In triangle XYZ, A and B are midpoints of XY and XZ. If YZ=14 cm and AB=2y+1, find y.", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "✅ In triangle ABC, D is midpoint of AB. DE || BC. If AD=3 cm and AE=4 cm, AC=?", "options": {"A": "4 cm", "B": "6 cm", "C": "8 cm", "D": "12 cm"}, "correct_answer": "C"},
    {"id": 36, "difficulty": "medium", "question": "📏 In triangle PQR, S and T are midpoints of PQ and PR. If ST=5 cm and QR=4x, find x.", "options": {"A": "2", "B": "2.5", "C": "3", "D": "5"}, "correct_answer": "B"},
    {"id": 37, "difficulty": "medium", "question": "🔺 In triangle ABC, D, E, F are midpoints. Then lines AD, BE, CF are...", "options": {"A": "medians", "B": "midsegments", "C": "altitudes", "D": "angle bisectors"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "✅ In triangle ABC, D and E are midpoints of AB and AC. If BC=12 cm and DE=2x-2, find x.", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "📐 In triangle LMN, P, Q, R are midpoints. If perimeter of triangle PQR=18 cm, perimeter of triangle LMN=?", "options": {"A": "9 cm", "B": "18 cm", "C": "27 cm", "D": "36 cm"}, "correct_answer": "D"},
    {"id": 40, "difficulty": "medium", "question": "🔺 In triangle ABC, D is midpoint of AB. DE || BC. If BC=10 cm, DE=?", "options": {"A": "5 cm", "B": "10 cm", "C": "15 cm", "D": "20 cm"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "hard", "question": "📐 In triangle ABC, D and E are midpoints of AB and AC. F is midpoint of AD. G is midpoint of AE. If FG=3 cm, BC=?", "options": {"A": "6 cm", "B": "12 cm", "C": "24 cm", "D": "30 cm"}, "correct_answer": "B"},
    {"id": 42, "difficulty": "hard", "question": "🔺 In quadrilateral ABCD, P, Q, R, S are midpoints. If area of ABCD=48 cm², area of PQRS=?", "options": {"A": "12 cm²", "B": "24 cm²", "C": "36 cm²", "D": "48 cm²"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "hard", "question": "✅ In triangle ABC, D and E are midpoints of AB and AC. DE produced meets BC produced at F. If DE=6 cm, EF=?", "options": {"A": "3 cm", "B": "6 cm", "C": "12 cm", "D": "18 cm"}, "correct_answer": "B"},
    {"id": 44, "difficulty": "hard", "question": "📏 In triangle PQR, S and T are midpoints of PQ and PR. U and V are midpoints of PS and PT. If UV=2 cm, QR=?", "options": {"A": "4 cm", "B": "8 cm", "C": "12 cm", "D": "16 cm"}, "correct_answer": "D"},
    {"id": 45, "difficulty": "hard", "question": "🔺 In triangle ABC, D, E, F are midpoints of BC, CA, AB. If area of triangle DEF=12 cm², area of triangle ABC=?", "options": {"A": "24 cm²", "B": "36 cm²", "C": "48 cm²", "D": "60 cm²"}, "correct_answer": "C"},
    {"id": 46, "difficulty": "hard", "question": "✅ In triangle XYZ, A and B are midpoints of XY and XZ. C is midpoint of YZ. If AB=5 cm, BC=6 cm, CA=7 cm, perimeter of triangle XYZ=?", "options": {"A": "18 cm", "B": "24 cm", "C": "36 cm", "D": "48 cm"}, "correct_answer": "C"},
    {"id": 47, "difficulty": "hard", "question": "📐 In triangle ABC, D and E are midpoints of AB and AC. BE and CD intersect at G (centroid). If DE=8 cm, BC=?", "options": {"A": "8 cm", "B": "12 cm", "C": "16 cm", "D": "24 cm"}, "correct_answer": "C"},
    {"id": 48, "difficulty": "hard", "question": "🔺 In quadrilateral ABCD, diagonals AC and BD intersect at O. P, Q, R, S are midpoints of OA, OB, OC, OD. Then PQRS is a...", "options": {"A": "parallelogram", "B": "rectangle", "C": "rhombus", "D": "square"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "hard", "question": "✅ In triangle ABC, D is midpoint of BC. E is midpoint of AD. BE produced meets AC at F. Then AF= ? * AC.", "options": {"A": "1/2", "B": "1/3", "C": "1/4", "D": "2/3"}, "correct_answer": "B"},
    {"id": 50, "difficulty": "hard", "question": "📏 In triangle PQR, S and T are midpoints of PQ and PR. U is midpoint of QR. If ST=6 cm, TU=8 cm, SU=10 cm, then perimeter of triangle PQR=?", "options": {"A": "24 cm", "B": "36 cm", "C": "48 cm", "D": "60 cm"}, "correct_answer": "C"},
    {"id": 51, "difficulty": "hard", "question": "🔺 In triangle ABC, D, E, F are midpoints. If area of triangle ABC=64 cm², area of quadrilateral BDFE=?", "options": {"A": "16 cm²", "B": "24 cm²", "C": "32 cm²", "D": "48 cm²"}, "correct_answer": "C"},
    {"id": 52, "difficulty": "hard", "question": "✅ In triangle XYZ, A and B are midpoints of XY and XZ. If YZ=20 cm and AB=3x+2, find x.", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "hard", "question": "📐 In triangle ABC, D and E are midpoints of AB and AC. DE is extended to F such that DE=EF. Then BF || ?", "options": {"A": "AB", "B": "AC", "C": "BC", "D": "DE"}, "correct_answer": "B"},
    {"id": 54, "difficulty": "hard", "question": "🔺 In triangle PQR, S and T are midpoints of PQ and PR. If ∠Q=50°, ∠R=70°, then ∠STR=?", "options": {"A": "50°", "B": "60°", "C": "70°", "D": "80°"}, "correct_answer": "B"},
    {"id": 55, "difficulty": "hard", "question": "✅ In triangle ABC, D, E, F are midpoints. If AB=6 cm, BC=8 cm, CA=10 cm, then perimeter of triangle DEF=?", "options": {"A": "6 cm", "B": "8 cm", "C": "12 cm", "D": "24 cm"}, "correct_answer": "C"},
    {"id": 56, "difficulty": "hard", "question": "📏 In triangle ABC, D is midpoint of AB. DE || BC. If area of triangle ADE=25 cm², area of trapezium DBCE=?", "options": {"A": "25 cm²", "B": "50 cm²", "C": "75 cm²", "D": "100 cm²"}, "correct_answer": "C"},
    {"id": 57, "difficulty": "hard", "question": "🔺 In quadrilateral ABCD, P, Q, R, S are midpoints. If AC ⟂ BD, then PQRS is a...", "options": {"A": "parallelogram", "B": "rectangle", "C": "rhombus", "D": "square"}, "correct_answer": "B"},
    {"id": 58, "difficulty": "hard", "question": "✅ In triangle ABC, D and E are midpoints of AB and BC. F is a point on AC such that DF || BC. Then F is... of AC.", "options": {"A": "midpoint", "B": "endpoint", "C": "one-third point", "D": "not determined"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "hard", "question": "📐 In triangle PQR, S and T are midpoints of PQ and PR. If ST=6 cm and QR=10 cm, then triangle PQR is...", "options": {"A": "scalene", "B": "isosceles", "C": "equilateral", "D": "right-angled"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "hard", "question": "✅ In triangle ABC, D, E, F are midpoints. The ratio of area of triangle DEF to area of triangle ABC is...", "options": {"A": "1:2", "B": "1:3", "C": "1:4", "D": "1:6"}, "correct_answer": "C"}
  ]
}