{
  "title": "Conditions for Similarity - Grade 10 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Two triangles are similar if their corresponding angles are:", "options": {"A": "Complementary", "B": "Supplementary", "C": "Equal", "D": "Different"}, "correct_answer": "C"},
    {"id": 2, "difficulty": "easy", "question": "If two angles of one triangle are equal to two angles of another triangle, the triangles are:", "options": {"A": "Congruent", "B": "Similar", "C": "Equal", "D": "Different"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "Which similarity criterion requires all three corresponding angles to be equal?", "options": {"A": "SSS", "B": "SAS", "C": "AA", "D": "RHS"}, "correct_answer": "C"},
    {"id": 4, "difficulty": "easy", "question": "In ΔABC and ΔDEF, if ∠A=∠D and ∠B=∠E, then the triangles are:", "options": {"A": "Congruent", "B": "Similar", "C": "Equal", "D": "Not related"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "For SAS similarity, the included angle must be:", "options": {"A": "Right angle", "B": "Equal", "C": "Acute", "D": "Obtuse"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "If corresponding sides of two triangles are proportional, they are similar by:", "options": {"A": "AA criterion", "B": "SAS criterion", "C": "SSS criterion", "D": "AAA criterion"}, "correct_answer": "C"},
    {"id": 7, "difficulty": "easy", "question": "Two triangles with all angles equal are always:", "options": {"A": "Congruent", "B": "Similar", "C": "Equal", "D": "Isosceles"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "For two triangles to be similar, minimum how many angles must be equal?", "options": {"A": "1", "B": "2", "C": "3", "D": "All three"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "In ΔPQR and ΔXYZ, if PQ/XY=QR/YZ=PR/XZ, then they are similar by:", "options": {"A": "AA", "B": "SAS", "C": "SSS", "D": "RHS"}, "correct_answer": "C"},
    {"id": 10, "difficulty": "easy", "question": "If two sides of one triangle are proportional to two sides of another and included angles are equal, similarity is by:", "options": {"A": "AA", "B": "SAS", "C": "SSS", "D": "ASA"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "All equilateral triangles are:", "options": {"A": "Congruent", "B": "Similar", "C": "Equal", "D": "Right-angled"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "Two isosceles triangles are always similar if:", "options": {"A": "Base angles are equal", "B": "Vertex angles are equal", "C": "They have same base", "D": "They have same height"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "If ΔABC ~ ΔDEF by AA criterion, then:", "options": {"A": "∠A=∠D, ∠B=∠E", "B": "AB/DE=BC/EF", "C": "Both A and B", "D": "AB=DE, BC=EF"}, "correct_answer": "C"},
    {"id": 14, "difficulty": "easy", "question": "For SSS similarity, we need:", "options": {"A": "All angles equal", "B": "All sides proportional", "C": "Two sides proportional and included angle equal", "D": "Right angle and hypotenuse proportional"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "If two triangles are similar, their corresponding sides are:", "options": {"A": "Equal", "B": "Proportional", "C": "Parallel", "D": "Perpendicular"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "In similar triangles, ratio of corresponding altitudes equals:", "options": {"A": "Ratio of areas", "B": "Ratio of sides", "C": "Square of ratio of sides", "D": "Ratio of perimeters"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "If ΔABC ~ ΔPQR, then ∠C equals:", "options": {"A": "∠P", "B": "∠Q", "C": "∠R", "D": "90°"}, "correct_answer": "C"},
    {"id": 18, "difficulty": "easy", "question": "All circles are:", "options": {"A": "Congruent", "B": "Similar", "C": "Equal", "D": "Different"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "Two squares are always:", "options": {"A": "Congruent", "B": "Similar", "C": "Equal", "D": "Different"}, "correct_answer": "B"},
    {"id": 20, "difficulty": "easy", "question": "If ΔABC ~ ΔDEF and AB=6 cm, DE=9 cm, then similarity ratio is:", "options": {"A": "2:3", "B": "3:2", "C": "6:9", "D": "9:6"}, "correct_answer": "A"},
    
    {"id": 21, "difficulty": "medium", "question": "In ΔABC and ΔPQR, ∠A=∠P=50°, ∠B=∠Q=60°. Are the triangles similar? If yes, by which criterion?", "options": {"A": "Yes, by AA", "B": "Yes, by SAS", "C": "Yes, by SSS", "D": "No, not similar"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "In ΔABC and ΔDEF, AB/DE=BC/EF=3/4 and ∠B=∠E=70°. Are they similar? By which criterion?", "options": {"A": "Yes, by SAS", "B": "Yes, by SSS", "C": "Yes, by AA", "D": "No, not similar"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "Two triangles have sides 3,4,5 and 6,8,10. Are they similar? By which criterion?", "options": {"A": "Yes, by SSS", "B": "Yes, by SAS", "C": "Yes, by AA", "D": "No, not similar"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "In ΔABC, AB=8 cm, BC=10 cm, AC=12 cm. In ΔPQR, PQ=12 cm, QR=15 cm, PR=18 cm. Are they similar?", "options": {"A": "Yes", "B": "No", "C": "Cannot determine", "D": "Only if angles are equal"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "ΔABC has ∠A=40°, ∠B=80°. ΔPQR has ∠P=40°, ∠Q=60°. Are they similar?", "options": {"A": "Yes", "B": "No", "C": "Only if third angles are equal", "D": "Cannot determine"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "In ΔABC and ΔDEF, AB=6 cm, BC=8 cm, ∠B=70°. DE=9 cm, EF=12 cm, ∠E=70°. Are they similar? By which criterion?", "options": {"A": "Yes, by SAS", "B": "Yes, by SSS", "C": "Yes, by AA", "D": "No"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "Two triangles have angles 30°, 60°, 90° and 30°, 60°, 90°. Are they similar?", "options": {"A": "Yes, by AA", "B": "Yes, by AAA", "C": "Both A and B", "D": "No, need side information"}, "correct_answer": "C"},
    {"id": 28, "difficulty": "medium", "question": "In ΔABC, ∠A=50°, ∠B=60°. In ΔPQR, ∠P=50°, ∠R=70°. Are they similar?", "options": {"A": "Yes", "B": "No", "C": "Only if sides proportional", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "ΔABC has sides 5,12,13. ΔPQR has sides 10,24,26. Are they similar? If yes, find similarity ratio.", "options": {"A": "Yes, 1:2", "B": "Yes, 2:1", "C": "No", "D": "Yes, 5:10"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "In ΔABC and ΔXYZ, AB/XY=BC/YZ=2/3. If ∠B=∠Y=90°, are they similar? By which criterion?", "options": {"A": "Yes, by SAS", "B": "Yes, by RHS", "C": "Yes, by SSS", "D": "No"}, "correct_answer": "B"},
    {"id": 31, "difficulty": "medium", "question": "Two isosceles triangles have equal vertex angles. Are they always similar?", "options": {"A": "Yes", "B": "No", "C": "Only if base angles equal", "D": "Only if sides equal"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "In ΔABC and ΔPQR, AB=4 cm, BC=5 cm, CA=6 cm. PQ=6 cm, QR=7.5 cm, RP=9 cm. Are they similar?", "options": {"A": "Yes", "B": "No", "C": "Only if angles match", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "If two triangles have their corresponding sides in ratio 2:5, they are similar by:", "options": {"A": "AA", "B": "SAS", "C": "SSS", "D": "Cannot determine without angles"}, "correct_answer": "C"},
    {"id": 34, "difficulty": "medium", "question": "ΔABC has ∠A=65°, ∠B=35°. ΔDEF has ∠D=65°, ∠E=80°. Are they similar?", "options": {"A": "Yes", "B": "No", "C": "Only if ∠C=∠F", "D": "Cannot determine"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "In right triangles ABC and PQR, right angled at B and Q. If AB/QR=BC/PQ=3/4, are they similar?", "options": {"A": "Yes, by SAS", "B": "Yes, by RHS", "C": "Yes, by AA", "D": "No"}, "correct_answer": "B"},
    {"id": 36, "difficulty": "medium", "question": "Two triangles have perimeters 30 cm and 45 cm. If they are similar, what is ratio of their corresponding sides?", "options": {"A": "2:3", "B": "3:2", "C": "30:45", "D": "√30:√45"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "In ΔABC and ΔDEF, ∠A=∠D, AB/DE=AC/DF. What additional condition is needed for similarity?", "options": {"A": "∠B=∠E", "B": "∠C=∠F", "C": "Included angle equal", "D": "BC/EF equal"}, "correct_answer": "C"},
    {"id": 38, "difficulty": "medium", "question": "All equilateral triangles of different sizes are similar because:", "options": {"A": "All sides equal", "B": "All angles 60°", "C": "Both A and B", "D": "They have same shape"}, "correct_answer": "B"},
    {"id": 39, "difficulty": "medium", "question": "In ΔABC, AB=8, BC=6, AC=10. In ΔPQR, PQ=12, QR=9, PR=15. Are they similar? If yes, find ∠B if ∠Q=53°.", "options": {"A": "Yes, ∠B=53°", "B": "Yes, ∠B=37°", "C": "No", "D": "Yes, ∠B=90°"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "Two triangles are similar if corresponding sides are proportional and:", "options": {"A": "Corresponding angles are equal", "B": "One angle is right angle", "C": "They have same perimeter", "D": "They have same area"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "medium", "question": "In ΔABC and ΔPQR, if AB/PQ=BC/QR and ∠B=∠Q, are they similar?", "options": {"A": "Yes, by SAS", "B": "Yes, by SSS", "C": "Yes, by AA", "D": "No, need AC/PR ratio"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "medium", "question": "ΔABC has angles 40°, 60°, 80°. ΔDEF has angles 40°, 80°, 60°. Are they similar?", "options": {"A": "Yes", "B": "No", "C": "Only if sides match", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "Two right triangles are similar if:", "options": {"A": "One acute angle is equal", "B": "Hypotenuse and one side proportional", "C": "Both A and B", "D": "They have same area"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "medium", "question": "In ΔABC and ΔXYZ, ∠A=∠X=45°, AB/XY=AC/XZ=2/3. Are they similar?", "options": {"A": "Yes, by SAS", "B": "Yes, by AA", "C": "Yes, by SSS", "D": "No"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "medium", "question": "If two triangles have two pairs of corresponding angles equal, the third pair:", "options": {"A": "Must be equal", "B": "May be different", "C": "Is complementary", "D": "Is supplementary"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "medium", "question": "ΔABC ~ ΔPQR. If AB=6, BC=8, CA=10 and PQ=9, find QR and RP.", "options": {"A": "QR=12, RP=15", "B": "QR=10, RP=12", "C": "QR=11, RP=14", "D": "QR=13, RP=16"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "medium", "question": "Two triangles with sides 7,24,25 and 14,48,50 are:", "options": {"A": "Similar", "B": "Congruent", "C": "Both similar and congruent", "D": "Neither"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "medium", "question": "In ΔABC and ΔDEF, ∠A=∠D, AB=5, AC=7, DE=10, DF=14. Are they similar? By which criterion?", "options": {"A": "Yes, by SAS", "B": "Yes, by SSS", "C": "Yes, by AA", "D": "No"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "medium", "question": "All squares are similar because:", "options": {"A": "All angles 90°", "B": "All sides proportional", "C": "Both A and B", "D": "They have same area"}, "correct_answer": "C"},
    {"id": 50, "difficulty": "medium", "question": "In ΔABC and ΔPQR, if ∠A=∠P and AB/PQ=BC/QR, are they necessarily similar?", "options": {"A": "Yes", "B": "No", "C": "Only if ∠B=∠Q", "D": "Only if AC/PR same ratio"}, "correct_answer": "B"},
    {"id": 51, "difficulty": "medium", "question": "Two triangles have areas 36 cm² and 64 cm². If they are similar, ratio of their corresponding sides is:", "options": {"A": "6:8", "B": "3:4", "C": "36:64", "D": "√36:√64"}, "correct_answer": "B"},
    {"id": 52, "difficulty": "medium", "question": "In ΔABC, ∠A=70°, ∠B=50°. In ΔPQR, ∠P=70°, ∠Q=60°. Are they similar?", "options": {"A": "Yes", "B": "No", "C": "Only if ∠C=∠R", "D": "Cannot determine"}, "correct_answer": "B"},
    {"id": 53, "difficulty": "medium", "question": "For two polygons to be similar, necessary conditions are:", "options": {"A": "Corresponding angles equal", "B": "Corresponding sides proportional", "C": "Both A and B", "D": "Same number of sides"}, "correct_answer": "C"},
    {"id": 54, "difficulty": "medium", "question": "ΔABC has sides 9,12,15. ΔPQR has sides 12,16,20. Are they similar? If yes, similarity ratio?", "options": {"A": "Yes, 3:4", "B": "Yes, 4:3", "C": "No", "D": "Yes, 9:12"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "medium", "question": "In ΔABC and ΔDEF, AB/DE=BC/EF=CA/FD. This condition is for:", "options": {"A": "AA similarity", "B": "SAS similarity", "C": "SSS similarity", "D": "ASA similarity"}, "correct_answer": "C"},
    {"id": 56, "difficulty": "medium", "question": "Two triangles with angles 50°, 60°, 70° and 60°, 50°, 70° are:", "options": {"A": "Similar", "B": "Congruent", "C": "Both", "D": "Neither"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "medium", "question": "If ΔABC ~ ΔPQR by SAS, which pair must be equal?", "options": {"A": "∠A=∠P", "B": "∠B=∠Q", "C": "∠C=∠R", "D": "Included angle between proportional sides"}, "correct_answer": "D"},
    {"id": 58, "difficulty": "medium", "question": "In right triangles, if an acute angle of one equals acute angle of another, they are similar by:", "options": {"A": "AA", "B": "SAS", "C": "SSS", "D": "RHS"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "medium", "question": "ΔABC has AB=6, BC=8, ∠B=90°. ΔPQR has PQ=9, QR=12, ∠Q=90°. Are they similar?", "options": {"A": "Yes", "B": "No", "C": "Only if PR calculated", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "medium", "question": "All circles are similar because:", "options": {"A": "Same shape", "B": "Constant ratio radius to circumference", "C": "Both A and B", "D": "Same area formula"}, "correct_answer": "A"},
    {"id": 61, "difficulty": "medium", "question": "In ΔABC and ΔXYZ, if ∠A=∠X and AB/XY=AC/XZ, then for similarity we need:", "options": {"A": "∠B=∠Y", "B": "∠C=∠Z", "C": "BC/YZ same ratio", "D": "Included angle equal"}, "correct_answer": "D"},
    {"id": 62, "difficulty": "medium", "question": "Two triangles with perimeters 24 and 36 are similar. Ratio of their areas is:", "options": {"A": "2:3", "B": "4:9", "C": "√24:√36", "D": "24:36"}, "correct_answer": "B"},
    {"id": 63, "difficulty": "medium", "question": "ΔABC ~ ΔPQR. If AB=5, BC=12, AC=13 and PQ=10, find perimeter of ΔPQR.", "options": {"A": "60", "B": "50", "C": "40", "D": "30"}, "correct_answer": "A"},
    {"id": 64, "difficulty": "medium", "question": "In ΔABC and ΔDEF, ∠B=∠E=90°, AB/DE=BC/EF. Are they similar?", "options": {"A": "Yes, by RHS", "B": "Yes, by SAS", "C": "Yes, by AA", "D": "No"}, "correct_answer": "B"},
    {"id": 65, "difficulty": "medium", "question": "Two equilateral triangles are always similar because:", "options": {"A": "AAA criterion satisfied", "B": "SSS criterion satisfied", "C": "Both A and B", "D": "They are always congruent"}, "correct_answer": "C"},
    {"id": 66, "difficulty": "medium", "question": "In ΔABC, AB=8, AC=10, ∠A=60°. In ΔPQR, PQ=12, PR=15, ∠P=60°. Are they similar?", "options": {"A": "Yes", "B": "No", "C": "Only if BC/QR calculated", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 67, "difficulty": "medium", "question": "If two triangles have their corresponding sides in ratio k:1, they are similar by:", "options": {"A": "AA", "B": "SAS", "C": "SSS", "D": "All of these"}, "correct_answer": "C"},
    {"id": 68, "difficulty": "medium", "question": "ΔABC has angles 30°, 60°, 90°. ΔPQR has angles 30°, 60°, 90°. Are they similar?", "options": {"A": "Yes", "B": "No", "C": "Only if sides proportional", "D": "Only if both are right triangles"}, "correct_answer": "A"},
    {"id": 69, "difficulty": "medium", "question": "For SAS similarity, the angle must be:", "options": {"A": "Right angle", "B": "Included angle", "C": "Any angle", "D": "Largest angle"}, "correct_answer": "B"},
    {"id": 70, "difficulty": "medium", "question": "Two triangles are similar if ratio of corresponding sides is 2:3 and included angles are equal. This is:", "options": {"A": "AA similarity", "B": "SAS similarity", "C": "SSS similarity", "D": "ASA similarity"}, "correct_answer": "B"},
    {"id": 71, "difficulty": "medium", "question": "In ΔABC and ΔPQR, if ∠A=∠P and ∠B=∠Q, then:", "options": {"A": "ΔABC ~ ΔPQR", "B": "AB/PQ=BC/QR", "C": "Both A and B", "D": "Only A is true"}, "correct_answer": "C"},
    {"id": 72, "difficulty": "medium", "question": "All rectangles are:", "options": {"A": "Similar", "B": "Congruent", "C": "Neither always similar nor congruent", "D": "Always similar"}, "correct_answer": "C"},
    {"id": 73, "difficulty": "medium", "question": "If two triangles have two pairs of sides proportional and included angles equal, they are similar by:", "options": {"A": "AA", "B": "SAS", "C": "SSS", "D": "ASA"}, "correct_answer": "B"},
    {"id": 74, "difficulty": "medium", "question": "ΔABC has sides 6,8,10. ΔPQR has sides 9,12,15. Similarity ratio is:", "options": {"A": "2:3", "B": "3:2", "C": "6:9", "D": "√6:√9"}, "correct_answer": "A"},
    {"id": 75, "difficulty": "medium", "question": "In ΔABC and ΔDEF, ∠A=∠D=40°, AB=5, AC=7, DE=10, DF=14. They are similar by:", "options": {"A": "AA", "B": "SAS", "C": "SSS", "D": "ASA"}, "correct_answer": "B"},
    {"id": 76, "difficulty": "medium", "question": "Two triangles with angles 45°, 45°, 90° and 45°, 45°, 90° are:", "options": {"A": "Similar", "B": "Congruent", "C": "Both", "D": "Neither unless sides given"}, "correct_answer": "A"},
    {"id": 77, "difficulty": "medium", "question": "For AA similarity, we need:", "options": {"A": "Two angles equal", "B": "Three angles equal", "C": "Both A and B", "D": "One angle equal"}, "correct_answer": "A"},
    {"id": 78, "difficulty": "medium", "question": "If ΔABC ~ ΔPQR by SSS, then:", "options": {"A": "AB/PQ=BC/QR=AC/PR", "B": "∠A=∠P, ∠B=∠Q", "C": "Both A and B", "D": "Only A is true"}, "correct_answer": "C"},
    {"id": 79, "difficulty": "medium", "question": "All rhombuses are:", "options": {"A": "Similar", "B": "Congruent", "C": "Neither always similar", "D": "Always similar"}, "correct_answer": "C"},
    {"id": 80, "difficulty": "medium", "question": "In ΔABC and ΔXYZ, if AB/XY=BC/YZ and ∠B=∠Y, then they are similar by:", "options": {"A": "AA", "B": "SAS", "C": "SSS", "D": "Cannot determine"}, "correct_answer": "B"},
    
    {"id": 81, "difficulty": "hard", "question": "In ΔABC and ΔPQR, ∠A=∠P, ∠B=∠Q. If AB=6 cm, BC=8 cm, CA=10 cm and PQ=9 cm, find QR and RP. Also find ratio of areas.", "options": {"A": "QR=12, RP=15, area ratio=4:9", "B": "QR=10, RP=12, area ratio=4:9", "C": "QR=12, RP=15, area ratio=2:3", "D": "QR=10, RP=12, area ratio=2:3"}, "correct_answer": "A"},
    {"id": 82, "difficulty": "hard", "question": "Two similar triangles have corresponding sides in ratio 3:7. If area of smaller triangle is 54 cm², find area of larger triangle and ratio of their perimeters.", "options": {"A": "Area=294, perimeter ratio=3:7", "B": "Area=286, perimeter ratio=3:7", "C": "Area=294, perimeter ratio=9:49", "D": "Area=286, perimeter ratio=9:49"}, "correct_answer": "A"},
    {"id": 83, "difficulty": "hard", "question": "In ΔABC and ΔDEF, AB/DE=BC/EF=CA/FD=2/3. If perimeter of ΔABC is 24 cm, find perimeter of ΔDEF and area ratio if they are similar.", "options": {"A": "Perimeter=36, area ratio=4:9", "B": "Perimeter=32, area ratio=4:9", "C": "Perimeter=36, area ratio=2:3", "D": "Perimeter=32, area ratio=2:3"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "ΔABC ~ ΔPQR by SAS similarity with AB/PQ=BC/QR=3/5 and ∠B=∠Q. If area(ΔABC)=81 cm², find area(ΔPQR) and ratio of their corresponding altitudes.", "options": {"A": "Area=225, altitude ratio=3:5", "B": "Area=215, altitude ratio=3:5", "C": "Area=225, altitude ratio=9:25", "D": "Area=215, altitude ratio=9:25"}, "correct_answer": "A"},
    {"id": 85, "difficulty": "hard", "question": "Two triangles are similar with similarity ratio 4:9. If difference of their areas is 260 cm², find areas of both triangles.", "options": {"A": "64 and 324", "B": "60 and 320", "C": "68 and 328", "D": "72 and 332"}, "correct_answer": "A"},
    {"id": 86, "difficulty": "hard", "question": "In ΔABC and ΔXYZ, ∠A=∠X, ∠B=∠Y. If AB=8 cm, BC=12 cm, AC=16 cm and XY=12 cm, find perimeter of ΔXYZ and verify if they are similar by AA criterion.", "options": {"A": "Perimeter=54, Yes", "B": "Perimeter=48, Yes", "C": "Perimeter=54, No", "D": "Perimeter=48, No"}, "correct_answer": "A"},
    {"id": 87, "difficulty": "hard", "question": "Two similar triangles have perimeters 30 cm and 45 cm. If area of larger triangle is 135 cm², find area of smaller triangle and ratio of their corresponding medians.", "options": {"A": "Area=60, median ratio=2:3", "B": "Area=65, median ratio=2:3", "C": "Area=60, median ratio=4:9", "D": "Area=65, median ratio=4:9"}, "correct_answer": "A"},
    {"id": 88, "difficulty": "hard", "question": "ΔABC ~ ΔPQR by SSS with AB=6, BC=8, CA=10 and PQ=9, QR=12, RP=15. Find ratio of their altitudes drawn from A and P respectively.", "options": {"A": "2:3", "B": "3:2", "C": "4:9", "D": "9:4"}, "correct_answer": "A"},
    {"id": 89, "difficulty": "hard", "question": "Two triangles have areas 100 cm² and 400 cm². If they are similar, find ratio of their corresponding sides and perimeters.", "options": {"A": "Sides 1:2, perimeters 1:2", "B": "Sides 1:4, perimeters 1:4", "C": "Sides 1:2, perimeters 1:4", "D": "Sides 1:4, perimeters 1:2"}, "correct_answer": "A"},
    {"id": 90, "difficulty": "hard", "question": "In ΔABC and ΔDEF, ∠A=∠D=65°, ∠B=∠E=45°. If AB=12 cm, BC=15 cm, CA=18 cm and DE=18 cm, find EF and FD. Also verify if triangles are similar.", "options": {"A": "EF=22.5, FD=27, Yes", "B": "EF=21, FD=25, Yes", "C": "EF=22.5, FD=27, No", "D": "EF=21, FD=25, No"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "Two similar triangles have corresponding medians in ratio 5:8. Find ratio of their areas and perimeters.", "options": {"A": "Areas 25:64, perimeters 5:8", "B": "Areas 5:8, perimeters 25:64", "C": "Areas 25:64, perimeters 25:64", "D": "Areas 5:8, perimeters 5:8"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "ΔABC ~ ΔXYZ by AA criterion. If AB=8, BC=10, CA=12 and XY=12, find YZ and ZX. Also find ratio of their altitudes.", "options": {"A": "YZ=15, ZX=18, ratio=2:3", "B": "YZ=14, ZX=16, ratio=2:3", "C": "YZ=15, ZX=18, ratio=4:9", "D": "YZ=14, ZX=16, ratio=4:9"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "Two triangles are similar with similarity ratio 3:5. If sum of their areas is 272 cm², find both areas.", "options": {"A": "72 and 200", "B": "75 and 197", "C": "78 and 194", "D": "81 and 191"}, "correct_answer": "A"},
    {"id": 94, "difficulty": "hard", "question": "In ΔABC and ΔPQR, AB/PQ=BC/QR=3/4 and ∠B=∠Q=70°. If area(ΔABC)=108 cm², find area(ΔPQR) and perimeter of ΔPQR if perimeter of ΔABC=36 cm.", "options": {"A": "Area=192, perimeter=48", "B": "Area=188, perimeter=46", "C": "Area=192, perimeter=46", "D": "Area=188, perimeter=48"}, "correct_answer": "A"},
    {"id": 95, "difficulty": "hard", "question": "Two similar triangles have perimeters in ratio 2:3. If area of smaller triangle is 48 cm², find area of larger triangle and ratio of their corresponding altitudes.", "options": {"A": "Area=108, altitude ratio=2:3", "B": "Area=104, altitude ratio=2:3", "C": "Area=108, altitude ratio=4:9", "D": "Area=104, altitude ratio=4:9"}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "ΔABC ~ ΔDEF by SAS with AB/DE=AC/DF=5/7 and ∠A=∠D. If area(ΔABC)=125 cm², find area(ΔDEF) and ratio of BC:EF.", "options": {"A": "Area=245, BC:EF=5:7", "B": "Area=240, BC:EF=5:7", "C": "Area=245, BC:EF=25:49", "D": "Area=240, BC:EF=25:49"}, "correct_answer": "A"},
    {"id": 97, "difficulty": "hard", "question": "Two triangles have areas 144 cm² and 225 cm². If they are similar, find ratio of their corresponding sides, medians, and altitudes.", "options": {"A": "12:15, 12:15, 12:15", "B": "144:225, 144:225, 144:225", "C": "√144:√225, √144:√225, √144:√225", "D": "12²:15², 12²:15², 12²:15²"}, "correct_answer": "A"},
    {"id": 98, "difficulty": "hard", "question": "In ΔABC and ΔXYZ, ∠A=∠X, ∠B=∠Y. If AB=10, BC=14, CA=18 and XY=15, find perimeter of ΔXYZ and verify similarity.", "options": {"A": "Perimeter=63, Yes", "B": "Perimeter=60, Yes", "C": "Perimeter=63, No", "D": "Perimeter=60, No"}, "correct_answer": "A"},
    {"id": 99, "difficulty": "hard", "question": "Two similar triangles have corresponding sides in ratio 2:5. If difference of their perimeters is 36 cm, find both perimeters.", "options": {"A": "24 and 60", "B": "26 and 62", "C": "28 and 64", "D": "30 and 66"}, "correct_answer": "A"},
    {"id": 100, "difficulty": "hard", "question": "ΔABC ~ ΔPQR with similarity ratio 3:8. If area(ΔABC) is 165 cm² less than area(ΔPQR), find both areas.", "options": {"A": "ABC=45, PQR=320", "B": "ABC=48, PQR=324", "C": "ABC=45, PQR=315", "D": "ABC=48, PQR=320"}, "correct_answer": "A"}
  ]
}