{
  "title": "Construction of similar triangles - Grade 10 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "🔺 Similar triangles have: ⭐", "options": {"A": "Same size", "B": "Same shape", "C": "Same area", "D": "Same perimeter"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "📐 For similar triangles, corresponding angles are: 🎯", "options": {"A": "Equal", "B": "Different", "C": "Complementary", "D": "Supplementary"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "⚡ Scale factor 2 means new triangle is: 🔄", "options": {"A": "Half size", "B": "Double size", "C": "Same size", "D": "Triple size"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "🎨 To construct similar triangle, we need: ✏️", "options": {"A": "Only angles", "B": "Only sides", "C": "Scale factor", "D": "Only area"}, "correct_answer": "C"},
    {"id": 5, "difficulty": "easy", "question": "🔍 Similar triangles symbol: 📐", "options": {"A": "≡", "B": "∼", "C": "≅", "D": "≈"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "📏 If scale factor=1, triangles are: 🤔", "options": {"A": "Similar", "B": "Congruent", "C": "Different", "D": "Rotated"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "💫 Corresponding sides of similar triangles are: ⚖️", "options": {"A": "Equal", "B": "Proportional", "C": "Parallel", "D": "Perpendicular"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "🎯 AAA similarity means: 🔢", "options": {"A": "All sides equal", "B": "All angles equal", "C": "Two angles equal", "D": "One angle equal"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "✂️ To construct similar Δ, first step: 1️⃣", "options": {"A": "Draw original triangle", "B": "Measure scale factor", "C": "Draw angles", "D": "Calculate area"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "🔺 Scale factor 0.5 gives triangle: 📊", "options": {"A": "Larger", "B": "Smaller", "C": "Same", "D": "Rotated"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "🌈 If ΔABC∼ΔDEF, then AB/DE = ? 📐", "options": {"A": "BC/EF", "B": "AC/DF", "C": "Both A and B", "D": "Neither"}, "correct_answer": "C"},
    {"id": 12, "difficulty": "easy", "question": "🎨 Basic proportionality theorem is also called: 📚", "options": {"A": "Pythagoras theorem", "B": "Thales theorem", "C": "Euler theorem", "D": "Apollonius theorem"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "⚡ For construction, we use scale factor to: 🔧", "options": {"A": "Multiply side lengths", "B": "Divide angles", "C": "Add areas", "D": "Subtract perimeters"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "📏 Similar triangles have same: 🎭", "options": {"A": "Shape ratio", "B": "Area", "C": "Perimeter", "D": "Height"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "🔍 If two triangles are similar, their altitudes are: 📐", "options": {"A": "Equal", "B": "Proportional", "C": "Same", "D": "Unrelated"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "💎 Ratio of areas of similar triangles = ? 📊", "options": {"A": "Scale factor", "B": "(Scale factor)²", "C": "(Scale factor)³", "D": "√(Scale factor)"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "🎯 To check similarity, minimum equal angles needed: 🔢", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "✏️ For SSS similarity, we need: 📏", "options": {"A": "All sides equal", "B": "All sides proportional", "C": "Two sides proportional", "D": "One side equal"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "🔺 SAS similarity requires: ⭐", "options": {"A": "One angle equal", "B": "Two angles equal", "C": "One angle equal & sides proportional", "D": "All sides proportional"}, "correct_answer": "C"},
    {"id": 20, "difficulty": "easy", "question": "📐 Equilateral triangles are always: 💫", "options": {"A": "Congruent", "B": "Similar", "C": "Different", "D": "Parallel"}, "correct_answer": "B"},
    
    {"id": 21, "difficulty": "medium", "question": "🔍 ΔABC∼ΔDEF with scale factor 3:2. If AB=9cm, DE=? 📏", "options": {"A": "4 cm", "B": "5 cm", "C": "6 cm", "D": "7 cm"}, "correct_answer": "C"},
    {"id": 22, "difficulty": "medium", "question": "🎨 Construct triangle similar to given Δ with scale factor 2/3. New triangle will be: 📐", "options": {"A": "Larger", "B": "Smaller", "C": "Same", "D": "Cannot say"}, "correct_answer": "B"},
    {"id": 23, "difficulty": "medium", "question": "⚡ ΔPQR∼ΔXYZ. PQ=6cm, QR=8cm, PR=10cm. If XY=9cm, find YZ? 🔢", "options": {"A": "10 cm", "B": "11 cm", "C": "12 cm", "D": "13 cm"}, "correct_answer": "C"},
    {"id": 24, "difficulty": "medium", "question": "📏 Two similar triangles have areas 25cm² and 64cm². Scale factor? 📊", "options": {"A": "5:8", "B": "8:5", "C": "25:64", "D": "64:25"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "💫 ΔABC has sides 5,12,13. Similar Δ has shortest side 10. Middle side? 🔺", "options": {"A": "20", "B": "22", "C": "24", "D": "26"}, "correct_answer": "C"},
    {"id": 26, "difficulty": "medium", "question": "🎯 Construct Δ similar to given ΔABC with scale factor 1.5. If BC=8cm, B'C'=? ✏️", "options": {"A": "10 cm", "B": "11 cm", "C": "12 cm", "D": "13 cm"}, "correct_answer": "C"},
    {"id": 27, "difficulty": "medium", "question": "🔍 Two triangles are similar. Corresponding sides 4cm & 6cm. Scale factor? ⚖️", "options": {"A": "2:3", "B": "3:2", "C": "4:6", "D": "6:4"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "🌈 In similar triangles, ratio of perimeters equals: 📐", "options": {"A": "Scale factor", "B": "Square of scale factor", "C": "Cube of scale factor", "D": "Square root of scale factor"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "✂️ ΔABC∼ΔDEF. AB=8cm, BC=15cm, CA=17cm. If DE=12cm, perimeter of ΔDEF? 🔢", "options": {"A": "30 cm", "B": "45 cm", "C": "60 cm", "D": "75 cm"}, "correct_answer": "C"},
    {"id": 30, "difficulty": "medium", "question": "📊 Similar triangles have areas 36cm² and 81cm². Ratio of corresponding sides? 📏", "options": {"A": "2:3", "B": "3:2", "C": "4:9", "D": "9:4"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "🔺 Scale factor k=3/4. New triangle area compared to original: 💎", "options": {"A": "9/16", "B": "3/4", "C": "4/3", "D": "16/9"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "🎨 For constructing similar triangle, which method uses parallel lines? 📐", "options": {"A": "AAA method", "B": "SSS method", "C": "Basic proportionality", "D": "Pythagoras method"}, "correct_answer": "C"},
    {"id": 33, "difficulty": "medium", "question": "⚡ ΔABC∼ΔPQR. ∠A=40°, ∠B=60°. ∠R=? 🔍", "options": {"A": "40°", "B": "60°", "C": "80°", "D": "100°"}, "correct_answer": "C"},
    {"id": 34, "difficulty": "medium", "question": "📏 Two triangles with angles 30°,60°,90° are: ⭐", "options": {"A": "Always congruent", "B": "Always similar", "C": "Sometimes similar", "D": "Never similar"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "💫 Construct Δ similar to right Δ with scale factor 2. If original hypotenuse=13cm, new hypotenuse=? 🎯", "options": {"A": "26 cm", "B": "24 cm", "C": "22 cm", "D": "20 cm"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "🔍 In similar triangles, ratio of medians equals: 📐", "options": {"A": "Scale factor", "B": "Square of scale factor", "C": "Cube of scale factor", "D": "Reciprocal of scale factor"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "🎨 ΔABC sides 7,24,25. Similar Δ has perimeter 112. Its sides? ✏️", "options": {"A": "14,48,50", "B": "21,72,75", "C": "28,96,100", "D": "35,120,125"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "🌈 Scale factor from Δ1 to Δ2 is 2. If Δ1 area=18cm², Δ2 area=? 📊", "options": {"A": "36 cm²", "B": "54 cm²", "C": "72 cm²", "D": "90 cm²"}, "correct_answer": "C"},
    {"id": 39, "difficulty": "medium", "question": "✂️ Two similar triangles have corresponding altitudes 8cm and 12cm. Scale factor? ⚖️", "options": {"A": "2:3", "B": "3:2", "C": "4:9", "D": "9:4"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "📐 ΔABC∼ΔDEF. AB=5cm, BC=12cm, AC=13cm. If DE=7.5cm, EF=? 🔢", "options": {"A": "15 cm", "B": "16 cm", "C": "17 cm", "D": "18 cm"}, "correct_answer": "D"},
    
    {"id": 41, "difficulty": "hard", "question": "🔺 Construct triangle similar to ΔABC with scale factor 5/3. If area ΔABC=27cm², new area? 📊", "options": {"A": "45 cm²", "B": "60 cm²", "C": "75 cm²", "D": "90 cm²"}, "correct_answer": "C"},
    {"id": 42, "difficulty": "hard", "question": "🎯 ΔABC∼ΔPQR. Areas 64cm² and 100cm². If BC=16cm, QR=? 📏", "options": {"A": "18 cm", "B": "20 cm", "C": "22 cm", "D": "24 cm"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "hard", "question": "💎 Two similar triangles have scale factor 3:5. Sum of their areas is 136cm². Smaller area? 🔍", "options": {"A": "36 cm²", "B": "40 cm²", "C": "44 cm²", "D": "48 cm²"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "hard", "question": "⚡ ΔABC∼ΔDEF. Perimeter ΔABC=30cm, perimeter ΔDEF=45cm. If AB=8cm, DE=? ✏️", "options": {"A": "10 cm", "B": "11 cm", "C": "12 cm", "D": "13 cm"}, "correct_answer": "C"},
    {"id": 45, "difficulty": "hard", "question": "📐 Construct similar triangle such that each side is 1.25 times original. Scale factor as fraction? 🎨", "options": {"A": "3/4", "B": "4/5", "C": "5/4", "D": "6/5"}, "correct_answer": "C"},
    {"id": 46, "difficulty": "hard", "question": "🔍 In two similar triangles, ratio of corresponding medians is 4:7. Ratio of their areas? 📊", "options": {"A": "16:49", "B": "4:7", "C": "2:√7", "D": "8:14"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "hard", "question": "🌈 ΔABC∼ΔDEF. ∠A=50°, ∠E=70°. Which angle in ΔABC equals ∠D? 🤔", "options": {"A": "∠A", "B": "∠B", "C": "∠C", "D": "None"}, "correct_answer": "C"},
    {"id": 48, "difficulty": "hard", "question": "💫 Areas of two similar triangles are 121cm² and 64cm². If side of first is 22cm, corresponding side of second? 📏", "options": {"A": "14 cm", "B": "15 cm", "C": "16 cm", "D": "17 cm"}, "correct_answer": "C"},
    {"id": 49, "difficulty": "hard", "question": "🎨 Construct Δ similar to given Δ with area 4/9 times original. Scale factor? 🔢", "options": {"A": "2/3", "B": "3/2", "C": "4/9", "D": "9/4"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "hard", "question": "✂️ ΔABC sides 6,8,10. Similar Δ has area 96cm². Perimeter of similar Δ? 📐", "options": {"A": "36 cm", "B": "42 cm", "C": "48 cm", "D": "54 cm"}, "correct_answer": "C"},
    {"id": 51, "difficulty": "hard", "question": "🔺 Scale factor k>1 gives triangle ______ than original: ⚡", "options": {"A": "Smaller", "B": "Larger", "C": "Congruent", "D": "Rotated"}, "correct_answer": "B"},
    {"id": 52, "difficulty": "hard", "question": "📊 Two similar triangles have perimeters 20cm and 35cm. If area of smaller=40cm², area of larger? 💎", "options": {"A": "110.25 cm²", "B": "122.5 cm²", "C": "135 cm²", "D": "140 cm²"}, "correct_answer": "B"},
    {"id": 53, "difficulty": "hard", "question": "🎯 In ΔABC∼ΔPQR, AB:BC=3:4. If PQ=9cm, QR=? 🔍", "options": {"A": "10 cm", "B": "11 cm", "C": "12 cm", "D": "13 cm"}, "correct_answer": "C"},
    {"id": 54, "difficulty": "hard", "question": "⚡ Construct triangle with sides 1.5 times given triangle. If original area=48cm², new area? 📏", "options": {"A": "72 cm²", "B": "96 cm²", "C": "108 cm²", "D": "120 cm²"}, "correct_answer": "C"},
    {"id": 55, "difficulty": "hard", "question": "🔍 ΔABC∼ΔDEF with scale factor 2/3. If altitude from A=12cm, corresponding altitude from D=? 📐", "options": {"A": "8 cm", "B": "9 cm", "C": "10 cm", "D": "11 cm"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "hard", "question": "💎 In similar triangles, ratio of inradii equals: 🎨", "options": {"A": "Scale factor", "B": "Square of scale factor", "C": "Cube of scale factor", "D": "Square root of scale factor"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "hard", "question": "📐 ΔABC sides 9,12,15. Similar Δ has side corresponding to 9 equal to 6. Area ratio? 📊", "options": {"A": "4:9", "B": "9:4", "C": "2:3", "D": "3:2"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "hard", "question": "🌈 Two similar triangles have corresponding sides (x+2) and (2x-1). If scale factor=3/2, find x? 🔢", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "D"},
    {"id": 59, "difficulty": "hard", "question": "🎯 Construct Δ similar to given triangle with scale factor 0.8. New perimeter compared to original: ✏️", "options": {"A": "64%", "B": "80%", "C": "125%", "D": "156%"}, "correct_answer": "B"},
    {"id": 60, "difficulty": "hard", "question": "🔺 Areas of three similar triangles are 16cm², 25cm², 36cm². Their sides are in ratio: ⭐", "options": {"A": "4:5:6", "B": "2:2.5:3", "C": "16:25:36", "D": "256:625:1296"}, "correct_answer": "A"}
  ]
}