{
  "title": "Congruence of Triangles - Grade 9 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Two triangles are congruent if:", "options": {"A": "They have same shape", "B": "They have same size and shape", "C": "They have same area", "D": "They have same perimeter"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "Congruent triangles have:", "options": {"A": "Equal angles only", "B": "Equal sides only", "C": "Equal angles and sides", "D": "Equal area only"}, "correct_answer": "C"},
    {"id": 3, "difficulty": "easy", "question": "Symbol for congruence is:", "options": {"A": "≈", "B": "≅", "C": "≡", "D": "~"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "If ΔABC ≅ ΔPQR, then AB corresponds to:", "options": {"A": "PQ", "B": "QR", "C": "RP", "D": "PR"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "If ΔABC ≅ ΔDEF, then ∠B corresponds to:", "options": {"A": "∠D", "B": "∠E", "C": "∠F", "D": "∠A"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "Congruent figures are always:", "options": {"A": "Similar", "B": "Equal in area", "C": "Different in shape", "D": "Different in size"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "If two triangles have same size and shape, they are:", "options": {"A": "Similar", "B": "Congruent", "C": "Equal", "D": "Equivalent"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "In congruent triangles, corresponding parts are:", "options": {"A": "Equal", "B": "Proportional", "C": "Different", "D": "Parallel"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "If ΔABC ≅ ΔXYZ, then BC = ?", "options": {"A": "XY", "B": "YZ", "C": "ZX", "D": "XZ"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "CPCT stands for:", "options": {"A": "Corresponding Parts of Congruent Triangles", "B": "Corresponding Parts of Congruent Terms", "C": "Corresponding Points of Congruent Triangles", "D": "Corresponding Properties of Congruent Triangles"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "Two triangles with all sides equal are:", "options": {"A": "Similar", "B": "Congruent", "C": "Different", "D": "Not determined"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "If ΔPQR ≅ ΔLMN, then ∠R = ?", "options": {"A": "∠L", "B": "∠M", "C": "∠N", "D": "∠P"}, "correct_answer": "C"},
    {"id": 13, "difficulty": "easy", "question": "Congruent triangles have equal:", "options": {"A": "Area", "B": "Perimeter", "C": "Both area and perimeter", "D": "Neither area nor perimeter"}, "correct_answer": "C"},
    {"id": 14, "difficulty": "easy", "question": "If two triangles are congruent, how many pairs of equal parts?", "options": {"A": "3", "B": "6", "C": "9", "D": "12"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "In ΔABC ≅ ΔDEF, if AB=5 cm, then DE=?", "options": {"A": "3 cm", "B": "4 cm", "C": "5 cm", "D": "6 cm"}, "correct_answer": "C"},
    {"id": 16, "difficulty": "easy", "question": "Two triangles with all angles equal are:", "options": {"A": "Always congruent", "B": "Sometimes congruent", "C": "Never congruent", "D": "Always similar"}, "correct_answer": "D"},
    {"id": 17, "difficulty": "easy", "question": "If ΔABC ≅ ΔPQR and ∠A=50°, then ∠P=?", "options": {"A": "40°", "B": "50°", "C": "60°", "D": "70°"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "Minimum conditions needed for triangle congruence:", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "C"},
    {"id": 19, "difficulty": "easy", "question": "Congruence is denoted by:", "options": {"A": "~", "B": "≈", "C": "≅", "D": "≡"}, "correct_answer": "C"},
    {"id": 20, "difficulty": "easy", "question": "If two triangles have same angles, they are:", "options": {"A": "Always congruent", "B": "Always similar", "C": "Never congruent", "D": "Never similar"}, "correct_answer": "B"},

    {"id": 21, "difficulty": "medium", "question": "In ΔABC and ΔDEF, AB=DE, BC=EF, AC=DF. Which congruence criterion?", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "For SAS congruence, angle must be:", "options": {"A": "Included angle", "B": "Any angle", "C": "Right angle", "D": "Largest angle"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "In ΔPQR and ΔXYZ, PQ=XY, ∠Q=∠Y, QR=YZ. Which criterion?", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "AAS"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "For ASA congruence, side must be:", "options": {"A": "Included side", "B": "Any side", "C": "Largest side", "D": "Smallest side"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "In ΔABC and ΔDEF, ∠B=∠E, BC=EF, ∠C=∠F. Which criterion?", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS"}, "correct_answer": "C"},
    {"id": 26, "difficulty": "medium", "question": "RHS congruence applies only to:", "options": {"A": "All triangles", "B": "Right triangles", "C": "Acute triangles", "D": "Obtuse triangles"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "In right triangles ABC and PQR, ∠B=∠Q=90°, AB=PQ, AC=PR. Which criterion?", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS"}, "correct_answer": "D"},
    {"id": 28, "difficulty": "medium", "question": "If ΔABC ≅ ΔPQR by SSS, then:", "options": {"A": "AB=PQ, BC=QR, AC=PR", "B": "AB=QR, BC=RP, CA=PQ", "C": "∠A=∠P, ∠B=∠Q, ∠C=∠R", "D": "AB=PQ, ∠B=∠Q, BC=QR"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "Two triangles with two sides and included angle equal are:", "options": {"A": "Always congruent", "B": "Sometimes congruent", "C": "Never congruent", "D": "Similar only"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "In ΔABC and ΔDEF, AB=DE, ∠A=∠D, ∠B=∠E. Which criterion?", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "AAS"}, "correct_answer": "C"},
    {"id": 31, "difficulty": "medium", "question": "If two right triangles have hypotenuse and one side equal, they are:", "options": {"A": "Similar", "B": "Congruent by RHS", "C": "Congruent by SAS", "D": "Not necessarily congruent"}, "correct_answer": "B"},
    {"id": 32, "difficulty": "medium", "question": "For triangles to be congruent by AAS, we need:", "options": {"A": "Two angles and included side", "B": "Two angles and any side", "C": "Two sides and included angle", "D": "Three sides"}, "correct_answer": "B"},
    {"id": 33, "difficulty": "medium", "question": "In ΔABC and ΔPQR, if AB=PQ, BC=QR, and ∠C=∠R, are they congruent?", "options": {"A": "Yes, by SAS", "B": "Yes, by SSS", "C": "No, not enough info", "D": "Yes, by RHS"}, "correct_answer": "C"},
    {"id": 34, "difficulty": "medium", "question": "Which is NOT a congruence criterion?", "options": {"A": "SSS", "B": "SAS", "C": "AAA", "D": "RHS"}, "correct_answer": "C"},
    {"id": 35, "difficulty": "medium", "question": "In ΔABC ≅ ΔDEF by ASA, if ∠A=40°, ∠B=60°, then ∠D=?", "options": {"A": "40°", "B": "60°", "C": "80°", "D": "100°"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "Two triangles with all three angles equal are:", "options": {"A": "Always congruent", "B": "Never congruent", "C": "Sometimes congruent", "D": "Always similar"}, "correct_answer": "D"},
    {"id": 37, "difficulty": "medium", "question": "If ΔABC ≅ ΔPQR by SAS, and AB=6 cm, BC=8 cm, ∠B=50°, then:", "options": {"A": "PQ=6 cm, QR=8 cm, ∠Q=50°", "B": "PQ=8 cm, QR=6 cm, ∠Q=50°", "C": "PQ=6 cm, QR=8 cm, ∠P=50°", "D": "PQ=6 cm, QR=8 cm, ∠R=50°"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "In congruent triangles, altitude to equal sides are:", "options": {"A": "Equal", "B": "Different", "C": "Parallel", "D": "Perpendicular"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "If two triangles have two angles and one side equal, they are:", "options": {"A": "Always congruent", "B": "Sometimes congruent", "C": "Never congruent", "D": "Similar only"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "Which condition ensures triangle congruence?", "options": {"A": "Three angles equal", "B": "Three sides equal", "C": "Two angles equal", "D": "Two sides equal"}, "correct_answer": "B"},
    {"id": 41, "difficulty": "medium", "question": "In ΔABC and ΔDEF, AB=DE, BC=EF, and ∠A=∠D. Are they congruent?", "options": {"A": "Yes, by SAS", "B": "Yes, by ASA", "C": "No, SSA not valid", "D": "Yes, by RHS"}, "correct_answer": "C"},
    {"id": 42, "difficulty": "medium", "question": "If two triangles are congruent, their medians are:", "options": {"A": "Equal", "B": "Different", "C": "Parallel", "D": "Perpendicular"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "In ΔPQR ≅ ΔXYZ by RHS, if ∠Q=∠Y=90°, PR=XZ=10 cm, PQ=6 cm, then XY=?", "options": {"A": "6 cm", "B": "8 cm", "C": "10 cm", "D": "12 cm"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "medium", "question": "Two isosceles triangles with equal base and equal base angles are:", "options": {"A": "Always congruent", "B": "Sometimes congruent", "C": "Never congruent", "D": "Similar only"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "medium", "question": "If ΔABC ≅ ΔDEF, and perimeter of ΔABC=24 cm, then perimeter of ΔDEF=?", "options": {"A": "12 cm", "B": "18 cm", "C": "24 cm", "D": "36 cm"}, "correct_answer": "C"},
    {"id": 46, "difficulty": "medium", "question": "In congruent triangles, corresponding altitudes are:", "options": {"A": "Equal", "B": "Different", "C": "Twice each other", "D": "Half each other"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "medium", "question": "If two triangles have two sides and non-included angle equal, they are:", "options": {"A": "Always congruent", "B": "Never congruent", "C": "Sometimes congruent", "D": "Always similar"}, "correct_answer": "C"},
    {"id": 48, "difficulty": "medium", "question": "In ΔABC and ΔPQR, if AB=PQ, ∠A=∠P, ∠C=∠R, they are congruent by:", "options": {"A": "ASA", "B": "AAS", "C": "SAS", "D": "SSS"}, "correct_answer": "B"},
    {"id": 49, "difficulty": "medium", "question": "If two right triangles have equal hypotenuse and one acute angle equal, they are:", "options": {"A": "Congruent by RHS", "B": "Congruent by AAS", "C": "Congruent by ASA", "D": "All of these"}, "correct_answer": "D"},
    {"id": 50, "difficulty": "medium", "question": "In ΔABC ≅ ΔDEF, if area of ΔABC=36 cm², area of ΔDEF=?", "options": {"A": "18 cm²", "B": "36 cm²", "C": "54 cm²", "D": "72 cm²"}, "correct_answer": "B"},
    {"id": 51, "difficulty": "medium", "question": "Which pair always gives congruent triangles?", "options": {"A": "Two equilateral triangles with side 5 cm", "B": "Two right triangles with hypotenuse 10 cm", "C": "Two isosceles triangles with base 6 cm", "D": "Two triangles with angles 30°, 60°, 90°"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "medium", "question": "If two triangles have equal area, they are:", "options": {"A": "Always congruent", "B": "Sometimes congruent", "C": "Never congruent", "D": "Always similar"}, "correct_answer": "B"},
    {"id": 53, "difficulty": "medium", "question": "In ΔABC and ΔPQR, AB=PQ=8 cm, BC=QR=6 cm, CA=RP=10 cm. They are:", "options": {"A": "Congruent by SSS", "B": "Congruent by SAS", "C": "Not necessarily congruent", "D": "Similar only"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "medium", "question": "If two triangles are congruent, their circumradii are:", "options": {"A": "Equal", "B": "Different", "C": "Twice", "D": "Half"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "medium", "question": "In ΔABC ≅ ΔDEF by SAS, if AB=5 cm, AC=7 cm, ∠A=60°, then:", "options": {"A": "DE=5 cm, DF=7 cm, ∠D=60°", "B": "DE=7 cm, DF=5 cm, ∠D=60°", "C": "DE=5 cm, EF=7 cm, ∠E=60°", "D": "DE=5 cm, DF=7 cm, ∠E=60°"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "medium", "question": "Two equilateral triangles with side 6 cm are:", "options": {"A": "Similar", "B": "Congruent", "C": "Both similar and congruent", "D": "Neither similar nor congruent"}, "correct_answer": "C"},
    {"id": 57, "difficulty": "medium", "question": "If two triangles have two angles and included side equal, they are congruent by:", "options": {"A": "ASA", "B": "AAS", "C": "SAS", "D": "SSS"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "medium", "question": "In ΔABC and ΔDEF, ∠A=∠D=90°, AB=DE, BC=EF. They are congruent by:", "options": {"A": "RHS", "B": "SAS", "C": "ASA", "D": "SSS"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "medium", "question": "If two triangles are congruent, their inradii are:", "options": {"A": "Equal", "B": "Different", "C": "Proportional", "D": "Unrelated"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "medium", "question": "Which is sufficient for triangle congruence?", "options": {"A": "AAA", "B": "SSA", "C": "ASA", "D": "ASS"}, "correct_answer": "C"},
    {"id": 61, "difficulty": "medium", "question": "In ΔABC ≅ ΔPQR, if AB=3x+2 and PQ=14, find x.", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "C"},
    {"id": 62, "difficulty": "medium", "question": "Two triangles with sides 5,6,7 cm and 5,6,8 cm are:", "options": {"A": "Congruent", "B": "Similar", "C": "Neither", "D": "Both"}, "correct_answer": "C"},
    {"id": 63, "difficulty": "medium", "question": "If ΔABC ≅ ΔDEF, and ∠A=55°, ∠B=65°, find ∠F.", "options": {"A": "55°", "B": "60°", "C": "65°", "D": "70°"}, "correct_answer": "B"},
    {"id": 64, "difficulty": "medium", "question": "In right triangles, if hypotenuse and one side equal, triangles are:", "options": {"A": "Similar", "B": "Congruent", "C": "Both", "D": "Neither"}, "correct_answer": "B"},
    {"id": 65, "difficulty": "medium", "question": "If two triangles have all three sides equal, they are:", "options": {"A": "Similar", "B": "Congruent", "C": "Both", "D": "Neither"}, "correct_answer": "C"},
    {"id": 66, "difficulty": "medium", "question": "In ΔABC and ΔPQR, AB=PQ, BC=QR, ∠B=∠Q. Which criterion?", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS"}, "correct_answer": "B"},
    {"id": 67, "difficulty": "medium", "question": "If two triangles are congruent, number of equal parts:", "options": {"A": "3", "B": "6", "C": "9", "D": "12"}, "correct_answer": "B"},
    {"id": 68, "difficulty": "medium", "question": "In ΔABC ≅ ΔDEF by ASA, if ∠A=40°, ∠C=70°, then ∠D=?", "options": {"A": "40°", "B": "70°", "C": "110°", "D": "180°"}, "correct_answer": "A"},
    {"id": 69, "difficulty": "medium", "question": "Two triangles with angles 30°,60°,90° and sides proportional are:", "options": {"A": "Congruent", "B": "Similar", "C": "Both", "D": "Neither"}, "correct_answer": "B"},
    {"id": 70, "difficulty": "medium", "question": "If ΔABC ≅ ΔPQR, and BC=2x+3, QR=11, find x.", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "B"},
    {"id": 71, "difficulty": "medium", "question": "In ΔABC and ΔDEF, ∠A=∠D, ∠B=∠E, BC=EF. They are congruent by:", "options": {"A": "ASA", "B": "AAS", "C": "SAS", "D": "SSS"}, "correct_answer": "B"},
    {"id": 72, "difficulty": "medium", "question": "If two triangles have equal area and equal base, they are:", "options": {"A": "Always congruent", "B": "Sometimes congruent", "C": "Never congruent", "D": "Always similar"}, "correct_answer": "B"},
    {"id": 73, "difficulty": "medium", "question": "In congruent triangles, corresponding medians are:", "options": {"A": "Equal", "B": "Different", "C": "Parallel", "D": "Perpendicular"}, "correct_answer": "A"},
    {"id": 74, "difficulty": "medium", "question": "If ΔABC ≅ ΔPQR by RHS, and ∠B=∠Q=90°, AC=PR=13 cm, AB=5 cm, find PQ.", "options": {"A": "5 cm", "B": "12 cm", "C": "13 cm", "D": "18 cm"}, "correct_answer": "A"},
    {"id": 75, "difficulty": "medium", "question": "Two triangles with sides 3,4,5 cm and 6,8,10 cm are:", "options": {"A": "Congruent", "B": "Similar", "C": "Both", "D": "Neither"}, "correct_answer": "B"},
    {"id": 76, "difficulty": "medium", "question": "In ΔABC ≅ ΔDEF, if ∠A=2x+10, ∠D=50°, find x.", "options": {"A": "10", "B": "15", "C": "20", "D": "25"}, "correct_answer": "C"},
    {"id": 77, "difficulty": "medium", "question": "If two triangles have two sides equal and included angle equal, they are:", "options": {"A": "Similar", "B": "Congruent", "C": "Both", "D": "Neither"}, "correct_answer": "B"},
    {"id": 78, "difficulty": "medium", "question": "In ΔABC and ΔPQR, AB=PQ, ∠A=∠P, ∠B=∠Q. They are:", "options": {"A": "Congruent by ASA", "B": "Congruent by AAS", "C": "Congruent by SAS", "D": "Not enough info"}, "correct_answer": "A"},
    {"id": 79, "difficulty": "medium", "question": "If two triangles are congruent, their perimeters are:", "options": {"A": "Equal", "B": "Different", "C": "Proportional", "D": "Unrelated"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "medium", "question": "In ΔABC ≅ ΔDEF by SSS, if AB=7 cm, BC=9 cm, CA=11 cm, then EF=?", "options": {"A": "7 cm", "B": "9 cm", "C": "11 cm", "D": "13 cm"}, "correct_answer": "B"},

    {"id": 81, "difficulty": "hard", "question": "In quadrilateral ABCD, AB=CD and AD=BC. Diagonals AC and BD intersect at O. Prove ΔAOB ≅ ΔCOD.", "options": {"A": "By SSS", "B": "By SAS", "C": "By ASA", "D": "By RHS"}, "correct_answer": "C"},
    {"id": 82, "difficulty": "hard", "question": "In ΔABC, AB=AC. D is midpoint of BC. Prove ΔABD ≅ ΔACD.", "options": {"A": "By SSS", "B": "By SAS", "C": "By RHS", "D": "By ASA"}, "correct_answer": "A"},
    {"id": 83, "difficulty": "hard", "question": "In right ΔABC, ∠B=90°. D is foot of perpendicular from B to AC. Prove ΔABD ∼ ΔBCD.", "options": {"A": "By AA", "B": "By SAS", "C": "By SSS", "D": "By RHS"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "Two circles intersect at A and B. Center of first circle is O, second is P. Prove ΔOAP ≅ ΔOBP.", "options": {"A": "By SSS", "B": "By SAS", "C": "By RHS", "D": "By ASA"}, "correct_answer": "A"},
    {"id": 85, "difficulty": "hard", "question": "In parallelogram ABCD, diagonal AC bisects ∠A and ∠C. Prove ΔABC ≅ ΔADC.", "options": {"A": "By SAS", "B": "By ASA", "C": "By SSS", "D": "By RHS"}, "correct_answer": "A"},
    {"id": 86, "difficulty": "hard", "question": "In ΔABC, D and E are points on AB and AC such that AD=AE and ∠BCD=∠CBE. Prove ΔABE ≅ ΔACD.", "options": {"A": "By SAS", "B": "By ASA", "C": "By AAS", "D": "By RHS"}, "correct_answer": "A"},
    {"id": 87, "difficulty": "hard", "question": "Two right triangles have equal hypotenuse and one acute angle equal. Prove they are congruent.", "options": {"A": "By ASA", "B": "By AAS", "C": "By RHS", "D": "All of these"}, "correct_answer": "D"},
    {"id": 88, "difficulty": "hard", "question": "In ΔABC, AB=AC. D and E are points on BC such that BD=CE. Prove ΔABD ≅ ΔACE.", "options": {"A": "By SAS", "B": "By SSS", "C": "By RHS", "D": "By ASA"}, "correct_answer": "A"},
    {"id": 89, "difficulty": "hard", "question": "In quadrilateral ABCD, AB||CD and AD||BC. Diagonals intersect at O. Prove ΔAOB ≅ ΔCOD.", "options": {"A": "By ASA", "B": "By AAS", "C": "By SAS", "D": "By SSS"}, "correct_answer": "A"},
    {"id": 90, "difficulty": "hard", "question": "In ΔABC, ∠B=2∠C. D is on BC such that AD bisects ∠BAC and AB=CD. Prove ΔABD ≅ ΔADC.", "options": {"A": "By SAS", "B": "By ASA", "C": "By SSS", "D": "By RHS"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "Two circles with centers O and P intersect at A and B. Prove OP is perpendicular bisector of AB.", "options": {"A": "Using congruent triangles", "B": "Using similar triangles", "C": "Using Pythagoras", "D": "Using area"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "In ΔABC, median AD is perpendicular to BC. Prove AB=AC.", "options": {"A": "Using SAS", "B": "Using RHS", "C": "Using SSS", "D": "Using ASA"}, "correct_answer": "B"},
    {"id": 93, "difficulty": "hard", "question": "In ΔABC, AB=AC. D and E are points on AB and AC such that BD=CE. Prove BE=CD.", "options": {"A": "Using SAS", "B": "Using SSS", "C": "Using ASA", "D": "Using RHS"}, "correct_answer": "A"},
    {"id": 94, "difficulty": "hard", "question": "Two chords AB and CD of circle intersect at E. If AE=BE and CE=DE, prove AC=BD.", "options": {"A": "Using SAS", "B": "Using SSS", "C": "Using ASA", "D": "Using RHS"}, "correct_answer": "A"},
    {"id": 95, "difficulty": "hard", "question": "In ΔABC, ∠A=90°. D is midpoint of BC. Prove AD=BD=CD.", "options": {"A": "Using congruent triangles", "B": "Using similar triangles", "C": "Using Pythagoras", "D": "Using area"}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "In quadrilateral ABCD, AB=AD and CB=CD. Prove AC bisects ∠A and ∠C.", "options": {"A": "Using SSS", "B": "Using SAS", "C": "Using ASA", "D": "Using RHS"}, "correct_answer": "A"},
    {"id": 97, "difficulty": "hard", "question": "In ΔABC, AB=AC. D is point on BC. DM ⟂ AB, DN ⟂ AC. Prove DM=DN.", "options": {"A": "Using AAS", "B": "Using RHS", "C": "Using SSS", "D": "Using SAS"}, "correct_answer": "B"},
    {"id": 98, "difficulty": "hard", "question": "Two triangles ABC and DEF have AB=DE, BC=EF, and median AM=median DN. Prove ΔABC ≅ ΔDEF.", "options": {"A": "By SSS", "B": "By SAS", "C": "Not necessarily congruent", "D": "By RHS"}, "correct_answer": "C"},
    {"id": 99, "difficulty": "hard", "question": "In ΔABC, ∠B=60°, ∠C=40°. D is on BC such that AD bisects ∠A. Prove AB>BD.", "options": {"A": "Using angle-side relationship", "B": "Using congruent triangles", "C": "Using similar triangles", "D": "Using Pythagoras"}, "correct_answer": "A"},
    {"id": 100, "difficulty": "hard", "question": "Two triangles have equal area and equal base. Are they always congruent?", "options": {"A": "Yes", "B": "No", "C": "Sometimes", "D": "Cannot determine"}, "correct_answer": "B"}
  ]
}