{
  "title": "Congruence Introduction (Triangles) - Grade 7 CBSE",
  "total_questions": 150,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "What does 'congruent' mean for triangles?", "options": {"A": "Same size but different shape", "B": "Same shape but different size", "C": "Same size and same shape", "D": "Different size and different shape"}, "correct_answer": "C"},
    {"id": 2, "difficulty": "easy", "question": "If ΔABC ≅ ΔDEF, which side corresponds to AB?", "options": {"A": "DE", "B": "EF", "C": "FD", "D": "BC"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "Which symbol is used for congruence?", "options": {"A": "≈", "B": "≅", "C": "=", "D": "~"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "If two triangles are congruent, their corresponding angles are:", "options": {"A": "Complementary", "B": "Supplementary", "C": "Equal", "D": "Unequal"}, "correct_answer": "C"},
    {"id": 5, "difficulty": "easy", "question": "How many criteria exist for triangle congruence?", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "D"},
    {"id": 6, "difficulty": "easy", "question": "SSS stands for:", "options": {"A": "Side-Side-Side", "B": "Side-Angle-Side", "C": "Angle-Side-Angle", "D": "Side-Side-Angle"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "If ΔPQR ≅ ΔXYZ, then ∠P corresponds to:", "options": {"A": "∠X", "B": "∠Y", "C": "∠Z", "D": "∠Q"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "Two triangles with all sides equal are congruent by which criterion?", "options": {"A": "SAS", "B": "ASA", "C": "SSS", "D": "RHS"}, "correct_answer": "C"},
    {"id": 9, "difficulty": "easy", "question": "RHS congruence applies to which type of triangles?", "options": {"A": "Acute triangles", "B": "Right triangles", "C": "Obtuse triangles", "D": "Equilateral triangles"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "If two angles and included side are equal, triangles are congruent by:", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "AAA"}, "correct_answer": "C"},
    {"id": 11, "difficulty": "easy", "question": "Can triangles be congruent if only angles are equal?", "options": {"A": "Yes, always", "B": "No, never", "C": "Only for right triangles", "D": "Only for equilateral triangles"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "What does SAS stand for?", "options": {"A": "Side-Angle-Side", "B": "Side-Side-Side", "C": "Angle-Side-Angle", "D": "Right-Hypotenuse-Side"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "If ΔABC ≅ ΔPQR, then BC corresponds to:", "options": {"A": "PQ", "B": "QR", "C": "RP", "D": "PR"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "AAA (Angle-Angle-Angle) ensures:", "options": {"A": "Congruence", "B": "Similarity", "C": "Equality", "D": "Perpendicularity"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "For ASA congruence, the side must be:", "options": {"A": "Between the angles", "B": "Opposite to an angle", "C": "The longest side", "D": "The shortest side"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "If two sides and included angle are equal, congruence is by:", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "AAS"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "Congruent triangles have equal:", "options": {"A": "Area only", "B": "Perimeter only", "C": "Both area and perimeter", "D": "Neither area nor perimeter"}, "correct_answer": "C"},
    {"id": 18, "difficulty": "easy", "question": "RHS stands for:", "options": {"A": "Right-Hypotenuse-Side", "B": "Right-Hypotenuse-Angle", "C": "Right-Angle-Hypotenuse-Side", "D": "Right-Angle-Side-Side"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "If ΔABC ≅ ΔDEF, then which is true?", "options": {"A": "AB = EF", "B": "BC = DE", "C": "AC = DF", "D": "∠A = ∠F"}, "correct_answer": "C"},
    {"id": 20, "difficulty": "easy", "question": "Two triangles with equal areas are:", "options": {"A": "Always congruent", "B": "Sometimes congruent", "C": "Never congruent", "D": "Always similar"}, "correct_answer": "B"},
    {"id": 21, "difficulty": "medium", "question": "In ΔABC and ΔPQR, AB = PQ, BC = QR, and ∠B = ∠Q. By which criterion are they congruent?", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS"}, "correct_answer": "B"},
    {"id": 22, "difficulty": "medium", "question": "If ΔXYZ ≅ ΔLMN and XY = 5 cm, what is LM?", "options": {"A": "2.5 cm", "B": "5 cm", "C": "10 cm", "D": "Cannot determine"}, "correct_answer": "B"},
    {"id": 23, "difficulty": "medium", "question": "In right triangles ABC and PQR, ∠B = ∠Q = 90°, AB = PQ, and AC = PR. They are congruent by:", "options": {"A": "SAS", "B": "ASA", "C": "RHS", "D": "SSS"}, "correct_answer": "C"},
    {"id": 24, "difficulty": "medium", "question": "Two triangles have sides 3,4,5 and 5,4,3. Are they congruent?", "options": {"A": "Yes, by SSS", "B": "Yes, by SAS", "C": "No", "D": "Yes, by RHS"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "In ΔABC ≅ ΔDEF, if ∠A = 50° and ∠B = 60°, what is ∠F?", "options": {"A": "50°", "B": "60°", "C": "70°", "D": "Cannot determine"}, "correct_answer": "C"},
    {"id": 26, "difficulty": "medium", "question": "For ASA congruence, if ∠A = ∠P, ∠B = ∠Q, then which sides must be equal?", "options": {"A": "AB = PQ", "B": "BC = QR", "C": "AC = PR", "D": "AB = QR"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "Two triangles with angles 30°, 60°, 90° and sides 3,4,5 and 6,8,10 are:", "options": {"A": "Congruent", "B": "Similar", "C": "Neither", "D": "Both congruent and similar"}, "correct_answer": "B"},
    {"id": 28, "difficulty": "medium", "question": "In ΔABC and ΔPQR, AB = PQ, ∠A = ∠P, ∠C = ∠R. They are congruent by:", "options": {"A": "ASA", "B": "AAS", "C": "SAS", "D": "SSS"}, "correct_answer": "B"},
    {"id": 29, "difficulty": "medium", "question": "If two triangles have two equal sides and one equal non-included angle, they are:", "options": {"A": "Always congruent", "B": "Sometimes congruent", "C": "Never congruent", "D": "Always similar"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "In congruent triangles, corresponding medians are:", "options": {"A": "Equal", "B": "Proportional", "C": "Perpendicular", "D": "Parallel"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "ΔABC ≅ ΔPQR. If AB = 7 cm and PR = 8 cm, what is AC?", "options": {"A": "7 cm", "B": "8 cm", "C": "15 cm", "D": "Cannot determine"}, "correct_answer": "B"},
    {"id": 32, "difficulty": "medium", "question": "Two equilateral triangles with sides 5 cm each are:", "options": {"A": "Congruent", "B": "Similar", "C": "Both", "D": "Neither"}, "correct_answer": "C"},
    {"id": 33, "difficulty": "medium", "question": "Which is NOT a congruence criterion?", "options": {"A": "SSS", "B": "SAS", "C": "AAA", "D": "RHS"}, "correct_answer": "C"},
    {"id": 34, "difficulty": "medium", "question": "In ΔABC ≅ ΔDEF, altitude from A = 6 cm. Altitude from D is:", "options": {"A": "3 cm", "B": "6 cm", "C": "12 cm", "D": "Cannot determine"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "Two right triangles have equal hypotenuse and one equal side. They are congruent by:", "options": {"A": "SAS", "B": "ASA", "C": "RHS", "D": "AAS"}, "correct_answer": "C"},
    {"id": 36, "difficulty": "medium", "question": "If ΔABC ≅ ΔPQR, perimeter of ΔABC = 24 cm, perimeter of ΔPQR = ?", "options": {"A": "12 cm", "B": "24 cm", "C": "48 cm", "D": "Cannot determine"}, "correct_answer": "B"},
    {"id": 37, "difficulty": "medium", "question": "For triangles to be congruent, minimum equal parts needed are:", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "B"},
    {"id": 38, "difficulty": "medium", "question": "In isosceles triangles with equal bases and equal base angles, congruence is by:", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS"}, "correct_answer": "B"},
    {"id": 39, "difficulty": "medium", "question": "ΔABC and ΔPQR have ∠A = ∠P = 90°, BC = QR, AC = PR. They are congruent by:", "options": {"A": "SAS", "B": "RHS", "C": "SSS", "D": "ASA"}, "correct_answer": "B"},
    {"id": 40, "difficulty": "medium", "question": "If two triangles have all angles equal, they are:", "options": {"A": "Congruent", "B": "Similar", "C": "Both", "D": "Cannot say"}, "correct_answer": "B"},
    {"id": 41, "difficulty": "medium", "question": "In ΔABC ≅ ΔDEF, area of ΔABC = 36 cm², area of ΔDEF = ?", "options": {"A": "18 cm²", "B": "36 cm²", "C": "72 cm²", "D": "144 cm²"}, "correct_answer": "B"},
    {"id": 42, "difficulty": "medium", "question": "Two triangles with sides 4,5,6 and 5,4,6 are:", "options": {"A": "Congruent by SSS", "B": "Congruent by SAS", "C": "Not congruent", "D": "Similar only"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "Which additional information makes ΔABC ≅ ΔPQR by ASA? Given: ∠B = ∠Q, BC = QR", "options": {"A": "∠A = ∠P", "B": "∠C = ∠R", "C": "AB = PQ", "D": "AC = PR"}, "correct_answer": "B"},
    {"id": 44, "difficulty": "medium", "question": "Congruent triangles placed differently are called:", "options": {"A": "Similar", "B": "Equivalent", "C": "Identical", "D": "Corresponding"}, "correct_answer": "C"},
    {"id": 45, "difficulty": "medium", "question": "If ΔABC ≅ ΔPQR, then ∠B + ∠C equals:", "options": {"A": "∠P + ∠Q", "B": "∠Q + ∠R", "C": "∠R + ∠P", "D": "∠P + ∠R"}, "correct_answer": "B"},
    {"id": 46, "difficulty": "medium", "question": "Two triangles with equal areas and equal bases have equal:", "options": {"A": "Heights", "B": "Perimeters", "C": "Angles", "D": "All sides"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "medium", "question": "In ΔABC and ΔDEF, AB = DE, BC = EF, ∠C = ∠F. Are they congruent?", "options": {"A": "Yes, by SAS", "B": "Yes, by SSS", "C": "Yes, by RHS", "D": "No, not necessarily"}, "correct_answer": "D"},
    {"id": 48, "difficulty": "medium", "question": "Which congruence criterion requires a right angle?", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS"}, "correct_answer": "D"},
    {"id": 49, "difficulty": "medium", "question": "If two triangles have equal perimeters, they are:", "options": {"A": "Always congruent", "B": "Sometimes congruent", "C": "Never congruent", "D": "Always similar"}, "correct_answer": "B"},
    {"id": 50, "difficulty": "medium", "question": "In ΔABC ≅ ΔPQR, median from A = 8 cm. Median from P = ?", "options": {"A": "4 cm", "B": "8 cm", "C": "16 cm", "D": "Cannot determine"}, "correct_answer": "B"},
    {"id": 51, "difficulty": "medium", "question": "Two triangles are congruent if two angles and included side of one equal two angles and ________ of the other.", "options": {"A": "Any side", "B": "Included side", "C": "Corresponding side", "D": "Opposite side"}, "correct_answer": "B"},
    {"id": 52, "difficulty": "medium", "question": "ΔABC and ΔPQR have AB = PQ, AC = PR, and ∠A > ∠P. Are they congruent?", "options": {"A": "Yes", "B": "No", "C": "Cannot determine", "D": "Only if right triangles"}, "correct_answer": "B"},
    {"id": 53, "difficulty": "medium", "question": "For SAS congruence, the angle must be:", "options": {"A": "Between the sides", "B": "Opposite to a side", "C": "Right angle", "D": "Acute angle"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "medium", "question": "Two triangles with equal corresponding sides but different orientations are:", "options": {"A": "Not congruent", "B": "Congruent", "C": "Similar", "D": "Equal"}, "correct_answer": "B"},
    {"id": 55, "difficulty": "medium", "question": "If ΔABC ≅ ΔDEF, and AB is the smallest side in ΔABC, then in ΔDEF:", "options": {"A": "DE is smallest", "B": "EF is smallest", "C": "FD is smallest", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "medium", "question": "In right triangles, if hypotenuse and one acute angle are equal, congruence is by:", "options": {"A": "RHS", "B": "ASA", "C": "SAS", "D": "AAS"}, "correct_answer": "D"},
    {"id": 57, "difficulty": "medium", "question": "Two triangles with sides 6,8,10 and 3,4,5 are:", "options": {"A": "Congruent", "B": "Similar", "C": "Both", "D": "Neither"}, "correct_answer": "B"},
    {"id": 58, "difficulty": "medium", "question": "If three sides of one triangle equal three sides of another, triangles are:", "options": {"A": "Similar", "B": "Congruent", "C": "Equal", "D": "Identical"}, "correct_answer": "B"},
    {"id": 59, "difficulty": "medium", "question": "In ΔABC ≅ ΔPQR, if AB = 2x+3 and PQ = 11, find x.", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "C"},
    {"id": 60, "difficulty": "medium", "question": "For RHS congruence, which must be equal?", "options": {"A": "Both legs", "B": "Hypotenuse and one leg", "C": "Both acute angles", "D": "One leg and one acute angle"}, "correct_answer": "B"},
    {"id": 61, "difficulty": "medium", "question": "Two triangles have equal areas and equal bases. Their heights are:", "options": {"A": "Equal", "B": "Different", "C": "Proportional", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 62, "difficulty": "medium", "question": "If ΔABC ≅ ΔPQR, and ∠A = 40°, ∠B = 80°, then ∠R = ?", "options": {"A": "40°", "B": "60°", "C": "80°", "D": "100°"}, "correct_answer": "B"},
    {"id": 63, "difficulty": "medium", "question": "In congruent triangles, corresponding angle bisectors are:", "options": {"A": "Equal", "B": "Proportional", "C": "Perpendicular", "D": "Parallel"}, "correct_answer": "A"},
    {"id": 64, "difficulty": "medium", "question": "Two isosceles triangles with equal bases and equal vertical angles are:", "options": {"A": "Congruent by SAS", "B": "Congruent by ASA", "C": "Congruent by SSS", "D": "Not necessarily congruent"}, "correct_answer": "D"},
    {"id": 65, "difficulty": "medium", "question": "If two triangles have two equal sides and equal included angle, they are:", "options": {"A": "Always similar", "B": "Always congruent", "C": "Sometimes congruent", "D": "Never congruent"}, "correct_answer": "B"},
    {"id": 66, "difficulty": "medium", "question": "ΔABC and ΔPQR have ∠A = ∠P = 90°, AB = PQ, BC = QR. They are congruent by:", "options": {"A": "RHS", "B": "SAS", "C": "SSS", "D": "ASA"}, "correct_answer": "A"},
    {"id": 67, "difficulty": "medium", "question": "For two triangles to be congruent, which is sufficient?", "options": {"A": "Two angles equal", "B": "Two sides equal", "C": "Three angles equal", "D": "Three sides equal"}, "correct_answer": "D"},
    {"id": 68, "difficulty": "medium", "question": "In ΔABC ≅ ΔDEF, if AB = 7 cm, BC = 5 cm, CA = 6 cm, then EF = ?", "options": {"A": "5 cm", "B": "6 cm", "C": "7 cm", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 69, "difficulty": "medium", "question": "Two equilateral triangles with sides 4 cm and 8 cm are:", "options": {"A": "Congruent", "B": "Similar", "C": "Both", "D": "Neither"}, "correct_answer": "B"},
    {"id": 70, "difficulty": "medium", "question": "If triangles are congruent, their circumradii are:", "options": {"A": "Equal", "B": "Proportional", "C": "Different", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 71, "difficulty": "medium", "question": "In ΔABC and ΔPQR, AB = PQ, ∠A = ∠P, BC = QR. Are they congruent?", "options": {"A": "Yes, by SAS", "B": "Yes, by SSS", "C": "Yes, by ASA", "D": "Not necessarily"}, "correct_answer": "A"},
    {"id": 72, "difficulty": "medium", "question": "For AAS congruence, the equal side is:", "options": {"A": "Between angles", "B": "Not between angles", "C": "Hypotenuse", "D": "Any side"}, "correct_answer": "B"},
    {"id": 73, "difficulty": "medium", "question": "Two right triangles with equal hypotenuses are:", "options": {"A": "Always congruent", "B": "Sometimes congruent", "C": "Never congruent", "D": "Always similar"}, "correct_answer": "B"},
    {"id": 74, "difficulty": "medium", "question": "If ΔABC ≅ ΔPQR, and altitude from A to BC = 9 cm, altitude from P to QR = ?", "options": {"A": "4.5 cm", "B": "9 cm", "C": "18 cm", "D": "27 cm"}, "correct_answer": "B"},
    {"id": 75, "difficulty": "medium", "question": "Triangles with equal corresponding sides have equal:", "options": {"A": "Areas", "B": "Perimeters", "C": "Both", "D": "Neither"}, "correct_answer": "C"},
    {"id": 76, "difficulty": "medium", "question": "In ΔABC ≅ ΔDEF, if AB = 2x+1 and DE = 9, find x.", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "B"},
    {"id": 77, "difficulty": "medium", "question": "Two triangles with sides 5,12,13 and 12,13,5 are:", "options": {"A": "Congruent", "B": "Similar", "C": "Both", "D": "Neither"}, "correct_answer": "A"},
    {"id": 78, "difficulty": "medium", "question": "For ASA congruence, we need:", "options": {"A": "Two angles and included side", "B": "Two sides and included angle", "C": "Three sides", "D": "Right angle, hypotenuse, side"}, "correct_answer": "A"},
    {"id": 79, "difficulty": "medium", "question": "If two triangles are congruent, their inradii are:", "options": {"A": "Equal", "B": "Different", "C": "Proportional", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "medium", "question": "ΔABC and ΔPQR have AB = PQ, ∠B = ∠Q, ∠C = ∠R. They are congruent by:", "options": {"A": "ASA", "B": "AAS", "C": "SAS", "D": "SSS"}, "correct_answer": "B"},
    {"id": 81, "difficulty": "hard", "question": "In quadrilateral ABCD, diagonal AC divides it into two congruent triangles ΔABC and ΔADC. Which is necessarily true?", "options": {"A": "AB = AD", "B": "BC = DC", "C": "∠ABC = ∠ADC", "D": "All of these"}, "correct_answer": "D"},
    {"id": 82, "difficulty": "hard", "question": "ΔABC ≅ ΔPQR. If AB = (2x+3) cm, PQ = 11 cm, BC = (3y-1) cm, QR = 8 cm, find x+y.", "options": {"A": "6", "B": "7", "C": "8", "D": "9"}, "correct_answer": "B"},
    {"id": 83, "difficulty": "hard", "question": "Two triangles have equal areas and equal perimeters. Are they necessarily congruent?", "options": {"A": "Yes", "B": "No", "C": "Only if right triangles", "D": "Only if isosceles"}, "correct_answer": "B"},
    {"id": 84, "difficulty": "hard", "question": "In ΔABC, D and E are points on AB and AC such that AD = AE and ∠ABE = ∠ACD. Prove ΔABE ≅ ΔACD by which criterion?", "options": {"A": "SAS", "B": "ASA", "C": "AAS", "D": "SSS"}, "correct_answer": "B"},
    {"id": 85, "difficulty": "hard", "question": "Two right triangles have equal areas and equal hypotenuses. Are they congruent?", "options": {"A": "Always", "B": "Sometimes", "C": "Never", "D": "Cannot determine"}, "correct_answer": "B"},
    {"id": 86, "difficulty": "hard", "question": "In ΔABC and ΔDEF, AB = DE, BC = EF, and median from A = median from D. Are triangles congruent?", "options": {"A": "Yes", "B": "No", "C": "Only if right triangles", "D": "Cannot determine"}, "correct_answer": "D"},
    {"id": 87, "difficulty": "hard", "question": "ΔABC ≅ ΔPQR. Area of ΔABC = 48 cm². If AB = 8 cm and PQ = 12 cm, find ratio of altitudes from C and R.", "options": {"A": "2:3", "B": "3:2", "C": "4:9", "D": "1:1"}, "correct_answer": "D"},
    {"id": 88, "difficulty": "hard", "question": "Two triangles have sides (a,b,c) and (b,c,a). Are they congruent?", "options": {"A": "Yes, always", "B": "No, never", "C": "Only if equilateral", "D": "Only if isosceles"}, "correct_answer": "A"},
    {"id": 89, "difficulty": "hard", "question": "In ΔABC, AB = AC. D is midpoint of BC. Which triangles are congruent?", "options": {"A": "ΔABD ≅ ΔACD", "B": "ΔABC ≅ ΔACB", "C": "Both", "D": "Neither"}, "correct_answer": "A"},
    {"id": 90, "difficulty": "hard", "question": "If two triangles have two equal sides and equal median to third side, are they congruent?", "options": {"A": "Yes", "B": "No", "C": "Only if right triangles", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "ΔABC ≅ ΔDEF. If ∠A:∠B:∠C = 2:3:4, find ∠D.", "options": {"A": "40°", "B": "60°", "C": "80°", "D": "100°"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "In quadrilateral ABCD, AB = CD and AD = BC. Diagonals intersect at O. Which triangles are congruent?", "options": {"A": "ΔAOB ≅ ΔCOD", "B": "ΔAOD ≅ ΔCOB", "C": "ΔABC ≅ ΔCDA", "D": "All of these"}, "correct_answer": "C"},
    {"id": 93, "difficulty": "hard", "question": "Two triangles have equal corresponding medians. Are they congruent?", "options": {"A": "Yes", "B": "No", "C": "Only if equilateral", "D": "Only if right triangles"}, "correct_answer": "B"},
    {"id": 94, "difficulty": "hard", "question": "In ΔABC, ∠A = 60°, AB = 8 cm, AC = 6 cm. In ΔPQR, ∠P = 60°, PQ = 6 cm, PR = 8 cm. Are they congruent?", "options": {"A": "Yes", "B": "No", "C": "Only if right triangles", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 95, "difficulty": "hard", "question": "If two triangles have equal perimeters and equal areas, are they congruent?", "options": {"A": "Yes", "B": "No", "C": "Only if right triangles", "D": "Only if isosceles"}, "correct_answer": "B"},
    {"id": 96, "difficulty": "hard", "question": "ΔABC ≅ ΔPQR. If altitude from A to BC = 10 cm and area of ΔABC = 60 cm², find QR.", "options": {"A": "6 cm", "B": "12 cm", "C": "10 cm", "D": "15 cm"}, "correct_answer": "B"},
    {"id": 97, "difficulty": "hard", "question": "Two right triangles have equal areas. Their hypotenuses are in ratio 2:1. Find ratio of their legs.", "options": {"A": "2:1", "B": "√2:1", "C": "4:1", "D": "1:√2"}, "correct_answer": "B"},
    {"id": 98, "difficulty": "hard", "question": "In ΔABC, D is on BC such that AD bisects ∠A. If AB = AC, which triangles are congruent?", "options": {"A": "ΔABD ≅ ΔADC", "B": "ΔABC ≅ ΔACB", "C": "Both", "D": "Neither"}, "correct_answer": "A"},
    {"id": 99, "difficulty": "hard", "question": "If two triangles have equal corresponding altitudes and equal bases, are they congruent?", "options": {"A": "Yes", "B": "No", "C": "Only if isosceles", "D": "Only if right triangles"}, "correct_answer": "B"},
    {"id": 100, "difficulty": "hard", "question": "ΔABC ≅ ΔDEF. If AB = 3x+2, DE = 14, BC = 2y-1, EF = 9, find x² + y².", "options": {"A": "13", "B": "25", "C": "34", "D": "41"}, "correct_answer": "C"}
 ,
 {"id":101,"difficulty":"easy","question":"If two triangles are congruent, their corresponding sides are:","options":{"A":"Equal","B":"Proportional","C":"Unequal","D":"Parallel"},"correct_answer":"A"},
    {"id":102,"difficulty":"easy","question":"Which criterion uses two sides and the included angle?","options":{"A":"SSS","B":"ASA","C":"SAS","D":"AAS"},"correct_answer":"C"},
    {"id":103,"difficulty":"easy","question":"If ΔABC ≅ ΔPQR, then angle C corresponds to:","options":{"A":"∠P","B":"∠Q","C":"∠R","D":"∠A"},"correct_answer":"C"},
    {"id":104,"difficulty":"easy","question":"Congruent triangles always have same:","options":{"A":"Shape only","B":"Size only","C":"Shape and size","D":"Area only"},"correct_answer":"C"},
    {"id":105,"difficulty":"easy","question":"Which of the following is NOT a congruence rule?","options":{"A":"SSS","B":"SAS","C":"ASA","D":"AAA"},"correct_answer":"D"},
    {"id":106,"difficulty":"easy","question":"If one triangle can be placed exactly on another, they are:","options":{"A":"Similar","B":"Congruent","C":"Equivalent","D":"Symmetric"},"correct_answer":"B"},
    {"id":107,"difficulty":"easy","question":"In congruent triangles, corresponding vertices are called:","options":{"A":"Equal vertices","B":"Same vertices","C":"Corresponding vertices","D":"Identical vertices"},"correct_answer":"C"},
    {"id":108,"difficulty":"easy","question":"RHS criterion applies only to:","options":{"A":"Acute triangles","B":"Isosceles triangles","C":"Right triangles","D":"Obtuse triangles"},"correct_answer":"C"},
    {"id":109,"difficulty":"easy","question":"If two triangles are congruent, their corresponding angles are:","options":{"A":"Supplementary","B":"Complementary","C":"Equal","D":"Right"},"correct_answer":"C"},
    {"id":110,"difficulty":"easy","question":"Which symbol represents congruence?","options":{"A":"=","B":"≈","C":"≅","D":"~"},"correct_answer":"C"},

    {"id":111,"difficulty":"medium","question":"In ΔABC ≅ ΔPQR, AB = 6 cm. What is PQ?","options":{"A":"3 cm","B":"6 cm","C":"9 cm","D":"Cannot determine"},"correct_answer":"B"},
    {"id":112,"difficulty":"medium","question":"Two triangles with sides 5,7,9 and 9,7,5 are congruent by:","options":{"A":"SAS","B":"ASA","C":"SSS","D":"RHS"},"correct_answer":"C"},
    {"id":113,"difficulty":"medium","question":"If two triangles are congruent, which of the following must be equal?","options":{"A":"Corresponding medians","B":"Corresponding heights","C":"Corresponding sides","D":"All of these"},"correct_answer":"D"},
    {"id":114,"difficulty":"medium","question":"In right triangles, equality of hypotenuse and one side ensures congruence by:","options":{"A":"SSS","B":"SAS","C":"ASA","D":"RHS"},"correct_answer":"D"},
    {"id":115,"difficulty":"medium","question":"Two triangles have equal bases and equal heights. They are:","options":{"A":"Always congruent","B":"Sometimes congruent","C":"Never congruent","D":"Always similar"},"correct_answer":"B"},
    {"id":116,"difficulty":"medium","question":"If ΔABC ≅ ΔDEF and ∠A = 45°, find ∠D.","options":{"A":"45°","B":"60°","C":"90°","D":"Cannot determine"},"correct_answer":"A"},
    {"id":117,"difficulty":"medium","question":"Which criterion uses two angles and a non-included side?","options":{"A":"ASA","B":"SAS","C":"AAS","D":"SSS"},"correct_answer":"C"},
    {"id":118,"difficulty":"medium","question":"Two equilateral triangles with side 6 cm each are:","options":{"A":"Congruent","B":"Similar","C":"Both","D":"Neither"},"correct_answer":"C"},
    {"id":119,"difficulty":"medium","question":"If ΔABC ≅ ΔPQR, then which pair is correct?","options":{"A":"AB = QR","B":"BC = PR","C":"AC = PQ","D":"AB = PQ"},"correct_answer":"D"},
    {"id":120,"difficulty":"medium","question":"If corresponding sides of two triangles are equal, triangles are congruent by:","options":{"A":"ASA","B":"SAS","C":"SSS","D":"RHS"},"correct_answer":"C"},

    {"id":121,"difficulty":"medium","question":"Two triangles have angles 40°, 60°, 80° each. They are:","options":{"A":"Congruent","B":"Similar","C":"Both","D":"Neither"},"correct_answer":"B"},
    {"id":122,"difficulty":"medium","question":"If ΔABC ≅ ΔPQR and perimeter of ΔABC is 30 cm, perimeter of ΔPQR is:","options":{"A":"15 cm","B":"30 cm","C":"60 cm","D":"Cannot determine"},"correct_answer":"B"},
    {"id":123,"difficulty":"medium","question":"In congruent triangles, corresponding angle bisectors are:","options":{"A":"Equal","B":"Parallel","C":"Proportional","D":"Unequal"},"correct_answer":"A"},
    {"id":124,"difficulty":"medium","question":"Two right triangles have equal areas and equal hypotenuses. They are:","options":{"A":"Always congruent","B":"Sometimes congruent","C":"Never congruent","D":"Always similar"},"correct_answer":"B"},
    {"id":125,"difficulty":"medium","question":"If ΔABC ≅ ΔDEF and AB is the longest side, then in ΔDEF the longest side is:","options":{"A":"DE","B":"EF","C":"FD","D":"Cannot determine"},"correct_answer":"A"},

    {"id":126,"difficulty":"hard","question":"In ΔABC, D is midpoint of BC and AB = AC. Which triangles are congruent?","options":{"A":"ΔABD ≅ ΔACD","B":"ΔABC ≅ ΔACB","C":"Both","D":"Neither"},"correct_answer":"A"},
    {"id":127,"difficulty":"hard","question":"Two triangles have equal corresponding medians. Are they congruent?","options":{"A":"Yes","B":"No","C":"Only if equilateral","D":"Only if right triangles"},"correct_answer":"B"},
    {"id":128,"difficulty":"hard","question":"If two triangles have equal areas and equal bases, which is necessarily equal?","options":{"A":"Sides","B":"Angles","C":"Heights","D":"Perimeters"},"correct_answer":"C"},
    {"id":129,"difficulty":"hard","question":"ΔABC ≅ ΔPQR. If AB = 2x+4 and PQ = 12, find x.","options":{"A":"2","B":"3","C":"4","D":"5"},"correct_answer":"B"},
    {"id":130,"difficulty":"hard","question":"Two triangles with sides (a,b,c) and (b,c,a) are congruent by:","options":{"A":"ASA","B":"SAS","C":"SSS","D":"RHS"},"correct_answer":"C"},
    {"id":131,"difficulty":"hard","question":"If ΔABC ≅ ΔDEF and ∠A:∠B:∠C = 1:2:3, find ∠D.","options":{"A":"30°","B":"60°","C":"90°","D":"120°"},"correct_answer":"A"},
    {"id":132,"difficulty":"hard","question":"Two right triangles have equal hypotenuses and equal areas. They are:","options":{"A":"Always congruent","B":"Sometimes congruent","C":"Never congruent","D":"Always similar"},"correct_answer":"B"},
    {"id":133,"difficulty":"hard","question":"In parallelogram ABCD, diagonal AC forms two congruent triangles because:","options":{"A":"SSS","B":"SAS","C":"ASA","D":"RHS"},"correct_answer":"B"},
    {"id":134,"difficulty":"hard","question":"If ΔABC ≅ ΔPQR and area of ΔABC = 64 cm², area of ΔPQR = ?","options":{"A":"32","B":"64","C":"128","D":"256"},"correct_answer":"B"},
    {"id":135,"difficulty":"hard","question":"Two triangles have equal perimeters and equal corresponding sides. They are:","options":{"A":"Similar","B":"Congruent","C":"Equivalent","D":"Isosceles"},"correct_answer":"B"},
    {"id":136,"difficulty":"hard","question":"In ΔABC, AB = AC and AD bisects ∠A. Which criterion proves ΔABD ≅ ΔACD?","options":{"A":"SSS","B":"SAS","C":"ASA","D":"AAS"},"correct_answer":"B"},
    {"id":137,"difficulty":"hard","question":"If two triangles have equal corresponding altitudes and equal bases, are they congruent?","options":{"A":"Yes","B":"No","C":"Only if right triangles","D":"Cannot determine"},"correct_answer":"B"},
    {"id":138,"difficulty":"hard","question":"ΔABC ≅ ΔPQR. If BC = 10 cm and area = 40 cm², find height corresponding to BC.","options":{"A":"4","B":"6","C":"8","D":"10"},"correct_answer":"A"},
    {"id":139,"difficulty":"hard","question":"Two triangles have equal sides but arranged differently. They are:","options":{"A":"Not congruent","B":"Congruent","C":"Similar","D":"Mirror images only"},"correct_answer":"B"},
    {"id":140,"difficulty":"hard","question":"If ΔABC ≅ ΔDEF and AB = 3x-2, DE = 13, find x.","options":{"A":"3","B":"4","C":"5","D":"6"},"correct_answer":"B"},

    {"id":141,"difficulty":"hard","question":"Which condition alone is sufficient to prove triangle congruence?","options":{"A":"Two sides","B":"Two angles","C":"Three sides","D":"Three angles"},"correct_answer":"C"},
    {"id":142,"difficulty":"hard","question":"In congruent triangles, ratio of corresponding sides is:","options":{"A":"1:1","B":"2:1","C":"Depends","D":"Cannot say"},"correct_answer":"A"},
    {"id":143,"difficulty":"hard","question":"If two triangles have equal circumradii and equal sides, they are:","options":{"A":"Congruent","B":"Similar","C":"Equivalent","D":"Isosceles"},"correct_answer":"A"},
    {"id":144,"difficulty":"hard","question":"Two triangles have equal corresponding sides and equal corresponding medians. They are:","options":{"A":"Congruent","B":"Similar","C":"Isosceles","D":"Right"},"correct_answer":"A"},
    {"id":145,"difficulty":"hard","question":"If ΔABC ≅ ΔPQR, which statement is false?","options":{"A":"AB = PQ","B":"∠A = ∠P","C":"Area equal","D":"Orientation same"},"correct_answer":"D"},
    {"id":146,"difficulty":"hard","question":"Two congruent triangles placed differently are called:","options":{"A":"Similar","B":"Identical","C":"Mirror images","D":"Equivalent"},"correct_answer":"C"},
    {"id":147,"difficulty":"hard","question":"If three sides of one triangle are equal to three sides of another triangle, angles are:","options":{"A":"Unequal","B":"Proportional","C":"Equal","D":"Right"},"correct_answer":"C"},
    {"id":148,"difficulty":"hard","question":"ΔABC ≅ ΔDEF. If perimeter of ΔDEF is 18 cm, perimeter of ΔABC is:","options":{"A":"9","B":"18","C":"36","D":"Cannot determine"},"correct_answer":"B"},
    {"id":149,"difficulty":"hard","question":"If ΔABC ≅ ΔPQR and AB = 5 cm, BC = 6 cm, CA = 7 cm, find PQ + QR.","options":{"A":"11","B":"12","C":"13","D":"18"},"correct_answer":"A"},
    {"id":150,"difficulty":"hard","question":"Two triangles have equal corresponding sides and equal areas. They are:","options":{"A":"Similar","B":"Congruent","C":"Equivalent","D":"Scalene"},"correct_answer":"B"}
 ]
}