{
  "title": "Congruence of Triangles SAS, SSS, ASA - Grade 7 CBSE",
  "total_questions": 150,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "What does SAS stand for in triangle congruence?", "options": {"A": "Side-Angle-Side", "B": "Side-Side-Side", "C": "Angle-Side-Angle", "D": "Angle-Angle-Side"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "Which congruence criterion requires all three sides to be equal?", "options": {"A": "SAS", "B": "SSS", "C": "ASA", "D": "RHS"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "In ASA criterion, what does the 'S' represent?", "options": {"A": "Side between angles", "B": "Side opposite angle", "C": "Any side", "D": "Hypotenuse"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "If two triangles have equal corresponding sides, they are congruent by:", "options": {"A": "SAS", "B": "SSS", "C": "ASA", "D": "AAS"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "For SAS congruence, the angle must be:", "options": {"A": "Included between sides", "B": "Right angle", "C": "Acute angle", "D": "Any angle"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "Which is NOT a triangle congruence criterion?", "options": {"A": "SSS", "B": "SAS", "C": "AAA", "D": "ASA"}, "correct_answer": "C"},
    {"id": 7, "difficulty": "easy", "question": "In ASA, the two angles must be:", "options": {"A": "Adjacent to the side", "B": "Right angles", "C": "Acute angles", "D": "Obtuse angles"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "If AB = DE, BC = EF, and AC = DF, which criterion proves ΔABC ≅ ΔDEF?", "options": {"A": "SAS", "B": "SSS", "C": "ASA", "D": "RHS"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "For two triangles to be congruent by SAS, we need:", "options": {"A": "Two sides and included angle", "B": "Two angles and included side", "C": "Three sides", "D": "Right angle and hypotenuse"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "If ∠A = ∠D, AB = DE, and ∠B = ∠E, which criterion applies?", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS"}, "correct_answer": "C"},
    {"id": 11, "difficulty": "easy", "question": "Which congruence criterion needs exactly one side?", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "None of these"}, "correct_answer": "D"},
    {"id": 12, "difficulty": "easy", "question": "If two triangles have two equal sides and equal included angle, they are congruent by:", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "AAS"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "For ASA congruence, we need:", "options": {"A": "Two angles and any side", "B": "Two angles and included side", "C": "Two sides and any angle", "D": "All three angles"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "Which criterion requires measurement of all three sides?", "options": {"A": "SAS", "B": "SSS", "C": "ASA", "D": "RHS"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "If triangles have two angles and the included side equal, they are congruent by:", "options": {"A": "SAS", "B": "SSS", "C": "ASA", "D": "AAA"}, "correct_answer": "C"},
    {"id": 16, "difficulty": "easy", "question": "In SAS, the side must be:", "options": {"A": "Opposite the angle", "B": "Adjacent to the angle", "C": "Included between angles", "D": "The longest side"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "Which congruence criterion is easiest to verify with ruler only?", "options": {"A": "SAS", "B": "SSS", "C": "ASA", "D": "AAS"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "For ASA, we need to know:", "options": {"A": "1 side and 2 angles", "B": "2 sides and 1 angle", "C": "3 sides", "D": "3 angles"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "If AB = PQ, ∠B = ∠Q, BC = QR, which criterion?", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS"}, "correct_answer": "B"},
    {"id": 20, "difficulty": "easy", "question": "Which requires a protractor for verification?", "options": {"A": "SSS only", "B": "SAS and ASA", "C": "SSS and SAS", "D": "All criteria"}, "correct_answer": "B"},
    
    {"id": 21, "difficulty": "medium", "question": "In ΔABC and ΔPQR, AB = PQ = 5 cm, BC = QR = 6 cm, ∠B = ∠Q = 60°. Are they congruent? If yes, by which criterion?", "options": {"A": "Yes, by SSS", "B": "Yes, by SAS", "C": "Yes, by ASA", "D": "Not congruent"}, "correct_answer": "B"},
    {"id": 22, "difficulty": "medium", "question": "Two triangles have sides 7 cm, 8 cm, 9 cm each. Are they congruent? By which criterion?", "options": {"A": "Yes, by SSS", "B": "Yes, by SAS", "C": "Yes, by ASA", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "In ΔABC and ΔDEF, ∠A = ∠D = 50°, ∠B = ∠E = 60°, and BC = EF = 7 cm. Are they congruent? By which criterion?", "options": {"A": "Yes, by SAS", "B": "Yes, by ASA", "C": "Yes, by SSS", "D": "Not congruent"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "If two triangles have two pairs of equal sides and equal included angles of 45°, they are congruent by:", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS"}, "correct_answer": "B"},
    {"id": 25, "difficulty": "medium", "question": "In ΔPQR and ΔXYZ, PQ = XY = 8 cm, QR = YZ = 6 cm, PR = XZ = 10 cm. Which criterion proves congruence?", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "Two triangles have angles 40°, 60°, 80° each and included side between 40° and 60° is 5 cm. They are congruent by:", "options": {"A": "SAS", "B": "ASA", "C": "SSS", "D": "AAA"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "In ΔABC and ΔLMN, AB = LM = 9 cm, ∠A = ∠L = 30°, AC = LN = 12 cm. Are they congruent? By which criterion?", "options": {"A": "Yes, by SAS", "B": "Yes, by SSS", "C": "Yes, by ASA", "D": "Not necessarily"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "If two triangles have all angles equal (AAA), are they always congruent?", "options": {"A": "Yes", "B": "No", "C": "Sometimes", "D": "Cannot say"}, "correct_answer": "B"},
    {"id": 29, "difficulty": "medium", "question": "In ΔABC and ΔPQR, ∠B = ∠Q = 90°, AB = PQ = 3 cm, BC = QR = 4 cm. Which criterion applies?", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "Two triangles have sides 5 cm, 12 cm, 13 cm each. They are congruent by:", "options": {"A": "SSS only", "B": "SAS only", "C": "Both SSS and SAS", "D": "RHS only"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "In ΔABC and ΔDEF, AB = DE = 7 cm, ∠A = ∠D = 65°, ∠C = ∠F = 45°. Are they congruent?", "options": {"A": "Yes, by ASA", "B": "Yes, by SAS", "C": "Yes, by AAS", "D": "Not enough information"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "For SAS congruence, the angle must be between the two sides. If angle is not included, can triangles still be congruent?", "options": {"A": "Always", "B": "Never", "C": "Sometimes", "D": "Cannot determine"}, "correct_answer": "C"},
    {"id": 33, "difficulty": "medium", "question": "Two triangles have two sides 6 cm and 8 cm, and non-included angle 30°. Are they always congruent?", "options": {"A": "Yes", "B": "No", "C": "Only if right triangles", "D": "Only if acute triangles"}, "correct_answer": "B"},
    {"id": 34, "difficulty": "medium", "question": "In isosceles triangles ABC and PQR, AB = AC = 10 cm, PQ = PR = 10 cm, and ∠A = ∠P = 50°. Are they congruent?", "options": {"A": "Yes, by SSS", "B": "Yes, by SAS", "C": "Yes, by ASA", "D": "Not necessarily"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "If two triangles have two angles 35° and 75° and included side 9 cm, they are congruent by:", "options": {"A": "SAS", "B": "ASA", "C": "SSS", "D": "AAS"}, "correct_answer": "B"},
    {"id": 36, "difficulty": "medium", "question": "Two equilateral triangles with side 6 cm each are congruent by:", "options": {"A": "SSS only", "B": "SAS only", "C": "ASA only", "D": "All criteria work"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "In ΔABC and ΔXYZ, AB = XY = 5 cm, BC = YZ = 7 cm, ∠B = ∠Y = 80°. Which additional information would prove congruence by SAS?", "options": {"A": "AC = XZ", "B": "∠A = ∠X", "C": "∠C = ∠Z", "D": "Already congruent by SAS"}, "correct_answer": "D"},
    {"id": 38, "difficulty": "medium", "question": "Two triangles have sides 4 cm, 5 cm, 6 cm and 4 cm, 5 cm, 7 cm. Are they congruent?", "options": {"A": "Yes", "B": "No", "C": "Sometimes", "D": "Cannot determine"}, "correct_answer": "B"},
    {"id": 39, "difficulty": "medium", "question": "For ASA, if we know two angles are 40° and 70°, what is the third angle?", "options": {"A": "60°", "B": "70°", "C": "80°", "D": "90°"}, "correct_answer": "B"},
    {"id": 40, "difficulty": "medium", "question": "In right triangles ABC and PQR, right angles at B and Q, AB = PQ = 3 cm, BC = QR = 4 cm. They are congruent by:", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS"}, "correct_answer": "B"},
    {"id": 41, "difficulty": "medium", "question": "Two triangles have sides in ratio 2:3:4. If one triangle has sides 4 cm, 6 cm, 8 cm, and other has 6 cm, 9 cm, 12 cm, are they congruent?", "options": {"A": "Yes", "B": "No", "C": "Similar but not congruent", "D": "Cannot determine"}, "correct_answer": "B"},
    {"id": 42, "difficulty": "medium", "question": "If ΔABC ≅ ΔPQR by SSS, and AB = 5 cm, BC = 6 cm, CA = 7 cm, what is PQ?", "options": {"A": "5 cm", "B": "6 cm", "C": "7 cm", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "For two triangles to be congruent by SAS, minimum measurements needed are:", "options": {"A": "2 sides + 1 angle", "B": "3 sides", "C": "2 angles + 1 side", "D": "1 side + 2 angles"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "medium", "question": "In ΔABC and ΔDEF, ∠A = ∠D, ∠B = ∠E, and AC = DF. Are they congruent?", "options": {"A": "Yes, by ASA", "B": "Yes, by AAS", "C": "Not necessarily", "D": "Cannot determine"}, "correct_answer": "B"},
    {"id": 45, "difficulty": "medium", "question": "Two triangles have equal areas. Are they necessarily congruent?", "options": {"A": "Yes", "B": "No", "C": "Only if right triangles", "D": "Only if isosceles"}, "correct_answer": "B"},
    {"id": 46, "difficulty": "medium", "question": "If two triangles are congruent by ASA, how many pairs of equal parts are known?", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "B"},
    {"id": 47, "difficulty": "medium", "question": "In ΔABC ≅ ΔXYZ by SAS, with AB = XY and ∠B = ∠Y. Which sides are equal?", "options": {"A": "AB = XY, BC = YZ", "B": "AB = XY, AC = XZ", "C": "BC = YZ, AC = XZ", "D": "All sides equal"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "medium", "question": "Two triangles have perimeters 24 cm each and corresponding sides equal. They are congruent by:", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "medium", "question": "In isosceles triangles with equal base angles and equal bases, they are congruent by:", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "All of these"}, "correct_answer": "C"},
    {"id": 50, "difficulty": "medium", "question": "If two triangles have two sides 8 cm, 10 cm and included angle 30°, then by SAS they are:", "options": {"A": "Always congruent", "B": "Sometimes congruent", "C": "Never congruent", "D": "Similar but not congruent"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "medium", "question": "For SSS congruence, how many independent measurements are needed?", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "B"},
    {"id": 52, "difficulty": "medium", "question": "In ΔABC and ΔPQR, AB = PQ, BC = QR, and ∠C = ∠R. Are they congruent?", "options": {"A": "Yes, by SAS", "B": "Yes, by SSS", "C": "Yes, by RHS", "D": "Not necessarily"}, "correct_answer": "D"},
    {"id": 53, "difficulty": "medium", "question": "Two triangles with angles 50°, 60°, 70° and sides proportional are:", "options": {"A": "Congruent", "B": "Similar", "C": "Both congruent and similar", "D": "Neither"}, "correct_answer": "B"},
    {"id": 54, "difficulty": "medium", "question": "If ΔABC ≅ ΔDEF by ASA, with ∠A = ∠D and ∠B = ∠E, which side is equal to AB?", "options": {"A": "DE", "B": "EF", "C": "FD", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "medium", "question": "For two right triangles, if hypotenuse and one side are equal, which criterion applies?", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS"}, "correct_answer": "D"},
    {"id": 56, "difficulty": "medium", "question": "In ΔABC and ΔPQR, if AB = PQ, BC = QR, and CA = RP, the correspondence is:", "options": {"A": "A↔P, B↔Q, C↔R", "B": "A↔Q, B↔R, C↔P", "C": "A↔R, B↔P, C↔Q", "D": "Any of these"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "medium", "question": "Two triangles have two equal sides 7 cm and 9 cm. For them to be congruent by SAS, the included angle must be:", "options": {"A": "Equal", "B": "Complementary", "C": "Supplementary", "D": "Any value"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "medium", "question": "If ΔABC ≅ ΔPQR by SAS, and AB = 6 cm, BC = 8 cm, ∠B = 90°, what is PR?", "options": {"A": "6 cm", "B": "8 cm", "C": "10 cm", "D": "Cannot determine"}, "correct_answer": "C"},
    {"id": 59, "difficulty": "medium", "question": "For ASA, if angles are 55° and 65°, the included side is opposite angle:", "options": {"A": "55°", "B": "65°", "C": "60°", "D": "120°"}, "correct_answer": "C"},
    {"id": 60, "difficulty": "medium", "question": "Two equilateral triangles with sides 5 cm and 6 cm are:", "options": {"A": "Congruent", "B": "Similar", "C": "Both", "D": "Neither"}, "correct_answer": "B"},
    {"id": 61, "difficulty": "medium", "question": "In ΔABC and ΔDEF, if ∠A = ∠D = 40°, ∠B = ∠E = 80°, and BC = EF = 12 cm, they are congruent by:", "options": {"A": "ASA", "B": "AAS", "C": "Both ASA and AAS", "D": "SAS"}, "correct_answer": "C"},
    {"id": 62, "difficulty": "medium", "question": "For SSS, the sum of any two sides must be:", "options": {"A": "Equal to third side", "B": "Greater than third side", "C": "Less than third side", "D": "Twice the third side"}, "correct_answer": "B"},
    {"id": 63, "difficulty": "medium", "question": "Two triangles with sides 3 cm, 4 cm, 5 cm and 4 cm, 3 cm, 5 cm are:", "options": {"A": "Congruent", "B": "Not congruent", "C": "Similar only", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 64, "difficulty": "medium", "question": "In ΔABC ≅ ΔXYZ by SAS, if AB = XY = 10 cm and ∠A = ∠X = 30°, which side equals AC?", "options": {"A": "XY", "B": "YZ", "C": "XZ", "D": "Cannot determine"}, "correct_answer": "C"},
    {"id": 65, "difficulty": "medium", "question": "If two triangles have equal areas and equal perimeters, are they congruent?", "options": {"A": "Always", "B": "Sometimes", "C": "Never", "D": "Cannot say"}, "correct_answer": "B"},
    {"id": 66, "difficulty": "medium", "question": "For ASA congruence, the side must be:", "options": {"A": "Between the two angles", "B": "Opposite one angle", "C": "The longest side", "D": "Any side"}, "correct_answer": "A"},
    {"id": 67, "difficulty": "medium", "question": "Two isosceles triangles with equal bases and equal base angles are congruent by:", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "All of these"}, "correct_answer": "C"},
    {"id": 68, "difficulty": "medium", "question": "In ΔABC and ΔPQR, AB = PQ, AC = PR, and ∠A = ∠P. They are congruent by:", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS"}, "correct_answer": "B"},
    {"id": 69, "difficulty": "medium", "question": "If two triangles have two equal angles and one equal side not included, they are congruent by:", "options": {"A": "ASA", "B": "AAS", "C": "SAS", "D": "SSS"}, "correct_answer": "B"},
    {"id": 70, "difficulty": "medium", "question": "For SAS, if sides are 5 cm and 7 cm, and included angle is 60°, the third side is:", "options": {"A": "√74 cm", "B": "√39 cm", "C": "√109 cm", "D": "Cannot determine exactly"}, "correct_answer": "D"},
    {"id": 71, "difficulty": "medium", "question": "Two triangles with sides 8 cm, 15 cm, 17 cm are:", "options": {"A": "Always congruent", "B": "Sometimes congruent", "C": "Right triangles", "D": "Acute triangles"}, "correct_answer": "C"},
    {"id": 72, "difficulty": "medium", "question": "In ΔABC ≅ ΔDEF by ASA, if ∠A = 50°, ∠B = 70°, and DE = 9 cm, what is AB?", "options": {"A": "5 cm", "B": "7 cm", "C": "9 cm", "D": "Cannot determine"}, "correct_answer": "C"},
    {"id": 73, "difficulty": "medium", "question": "For two triangles to be congruent, minimum conditions needed are:", "options": {"A": "3 sides equal", "B": "2 sides and included angle equal", "C": "2 angles and included side equal", "D": "Any of these"}, "correct_answer": "D"},
    {"id": 74, "difficulty": "medium", "question": "If ΔABC ≅ ΔPQR by SSS, and AB = 8 cm, BC = 10 cm, CA = 12 cm, what is perimeter of ΔPQR?", "options": {"A": "20 cm", "B": "24 cm", "C": "30 cm", "D": "36 cm"}, "correct_answer": "C"},
    {"id": 75, "difficulty": "medium", "question": "Two triangles have equal vertical angles and equal adjacent sides. They are congruent by:", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS"}, "correct_answer": "B"},
    {"id": 76, "difficulty": "medium", "question": "In right triangles, if legs are equal, they are congruent by:", "options": {"A": "SAS", "B": "RHS", "C": "Both SAS and RHS", "D": "SSS"}, "correct_answer": "A"},
    {"id": 77, "difficulty": "medium", "question": "For ASA, if two angles are 45° and 55°, the third angle is:", "options": {"A": "80°", "B": "90°", "C": "100°", "D": "110°"}, "correct_answer": "A"},
    {"id": 78, "difficulty": "medium", "question": "Two triangles with sides in ratio 1:1:√2 are:", "options": {"A": "Congruent if sides equal", "B": "Similar", "C": "Right isosceles", "D": "All of these"}, "correct_answer": "D"},
    {"id": 79, "difficulty": "medium", "question": "In ΔABC and ΔDEF, if ∠A = ∠D, ∠B = ∠E, and AB = DE, they are congruent by:", "options": {"A": "ASA", "B": "SAS", "C": "Both", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "medium", "question": "If two triangles are congruent by SAS, how many different SAS combinations are possible?", "options": {"A": "1", "B": "2", "C": "3", "D": "6"}, "correct_answer": "C"},
    
    {"id": 81, "difficulty": "hard", "question": "In quadrilateral ABCD and PQRS, AB = PQ, BC = QR, CD = RS, DA = SP, and diagonal AC = PR. Are the quadrilaterals necessarily congruent?", "options": {"A": "Yes, always", "B": "No, never", "C": "Yes, if angles also equal", "D": "Only if convex"}, "correct_answer": "C"},
    {"id": 82, "difficulty": "hard", "question": "Two triangles have sides a=8 cm, b=15 cm, c=17 cm and a'=15 cm, b'=8 cm, c'=17 cm. Are they congruent? If yes, by which criterion?", "options": {"A": "Yes, by SSS", "B": "Yes, by SAS", "C": "No, not congruent", "D": "Yes, by RHS"}, "correct_answer": "A"},
    {"id": 83, "difficulty": "hard", "question": "In ΔABC and ΔPQR, AB = PQ = 10 cm, ∠A = ∠P = 40°, and AC = PR = 12 cm. ∠C = 70°. Find ∠R if triangles are congruent by SAS.", "options": {"A": "40°", "B": "60°", "C": "70°", "D": "80°"}, "correct_answer": "C"},
    {"id": 84, "difficulty": "hard", "question": "Two triangles have two sides 12 cm and 16 cm. For them to be congruent, the third side must be:", "options": {"A": "4 cm", "B": "20 cm", "C": "28 cm", "D": "Between 4 cm and 28 cm"}, "correct_answer": "D"},
    {"id": 85, "difficulty": "hard", "question": "In ΔABC ≅ ΔXYZ by ASA. ∠A = (2x+10)°, ∠X = 50°, ∠B = (3y-20)°, ∠Y = 40°, and BC = (z+5) cm, YZ = 15 cm. Find x+y+z.", "options": {"A": "30", "B": "35", "C": "40", "D": "45"}, "correct_answer": "B"},
    {"id": 86, "difficulty": "hard", "question": "Two congruent triangles have sides in ratio 3:4:5. If perimeter is 60 cm, find area if it's a right triangle.", "options": {"A": "60 cm²", "B": "120 cm²", "C": "150 cm²", "D": "180 cm²"}, "correct_answer": "C"},
    {"id": 87, "difficulty": "hard", "question": "In ΔABC and ΔDEF, AB = DE, BC = EF, and ∠A = ∠D. Under what additional condition will they be congruent by SAS?", "options": {"A": "∠B = ∠E", "B": "∠C = ∠F", "C": "AC = DF", "D": "Already congruent"}, "correct_answer": "C"},
    {"id": 88, "difficulty": "hard", "question": "Two triangles have angles 30°, 60°, 90° and sides opposite 30° are 5 cm each. Are they congruent?", "options": {"A": "Yes, by ASA", "B": "Yes, by AAS", "C": "Yes, by SAS", "D": "Yes, by RHS"}, "correct_answer": "D"},
    {"id": 89, "difficulty": "hard", "question": "In ΔPQR and ΔSTU, PQ = ST = 8 cm, QR = TU = 6 cm, ∠Q = ∠T = 90°. PR = 10 cm. What must SU be for congruence by RHS?", "options": {"A": "6 cm", "B": "8 cm", "C": "10 cm", "D": "12 cm"}, "correct_answer": "C"},
    {"id": 90, "difficulty": "hard", "question": "Two isosceles triangles have equal bases 12 cm and equal vertical angles 40°. Are they necessarily congruent?", "options": {"A": "Yes", "B": "No", "C": "Only if legs equal", "D": "Only if height equal"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "In ΔABC ≅ ΔLMN by SAS. AB = (2x+3) cm, LM = 13 cm, BC = (3y-4) cm, MN = 17 cm, ∠B = (4z+5)°, ∠M = 65°. Find x+y+z.", "options": {"A": "20", "B": "23", "C": "27", "D": "29"}, "correct_answer": "C"},
    {"id": 92, "difficulty": "hard", "question": "Two triangles have sides a,b,c and a',b',c' with a/a' = b/b' = c/c' = k. For them to be congruent, k must be:", "options": {"A": "1", "B": ">1", "C": "<1", "D": "Any positive number"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "In quadrilateral ABCD ≅ quadrilateral PQRS by SSSS (all sides equal). If ∠A = 70°, ∠B = 110°, ∠C = 70°, what is ∠Q?", "options": {"A": "70°", "B": "110°", "C": "90°", "D": "Cannot determine"}, "correct_answer": "B"},
    {"id": 94, "difficulty": "hard", "question": "Two right triangles have hypotenuse 25 cm and one leg 7 cm. Are they congruent?", "options": {"A": "Yes, by RHS", "B": "Yes, by SSS", "C": "Yes, by SAS", "D": "Yes, by any criterion"}, "correct_answer": "A"},
    {"id": 95, "difficulty": "hard", "question": "In ΔABC and ΔPQR, AB/PQ = BC/QR = CA/RP = 1.5. If AB = 9 cm, find PQ.", "options": {"A": "4.5 cm", "B": "6 cm", "C": "9 cm", "D": "13.5 cm"}, "correct_answer": "B"},
    {"id": 96, "difficulty": "hard", "question": "Two triangles have equal areas and equal bases. Are they congruent?", "options": {"A": "Always", "B": "Sometimes", "C": "Never", "D": "Only if isosceles"}, "correct_answer": "B"},
    {"id": 97, "difficulty": "hard", "question": "In ΔABC ≅ ΔDEF by ASA. ∠A = (3x-10)°, ∠D = 50°, ∠B = (2y+20)°, ∠E = 80°, BC = (4z-3) cm, EF = 17 cm. Find x+y+z.", "options": {"A": "22", "B": "55", "C": "28", "D": "31"}, "correct_answer": "B"},
    {"id": 98, "difficulty": "hard", "question": "Two triangles have sides satisfying a²+b² = c² and a'²+b'² = c'² with a=a', b=b'. Are they congruent?", "options": {"A": "Yes, by RHS", "B": "Yes, by SSS", "C": "Yes, by SAS", "D": "Yes, by any criterion"}, "correct_answer": "B"},
    {"id": 99, "difficulty": "hard", "question": "In ΔPQR and ΔXYZ, PQ = XY, QR = YZ, and ∠P = ∠X. What additional condition makes them congruent by SAS?", "options": {"A": "∠Q = ∠Y", "B": "PR = XZ", "C": "∠R = ∠Z", "D": "Already congruent"}, "correct_answer": "B"},
    {"id": 100, "difficulty": "hard", "question": "Two equilateral triangles have sides in ratio 2:3. Their areas are in ratio:", "options": {"A": "2:3", "B": "4:9", "C": "√2:√3", "D": "8:27"}, "correct_answer": "B"}
  ,
 {"id":101,"difficulty":"easy","question":"Which congruence rule uses two sides and the angle between them?","options":{"A":"SSS","B":"ASA","C":"SAS","D":"AAA"},"correct_answer":"C"},
    {"id":102,"difficulty":"easy","question":"If three sides of one triangle are equal to three sides of another, the triangles are congruent by:","options":{"A":"ASA","B":"SAS","C":"SSS","D":"AAS"},"correct_answer":"C"},
    {"id":103,"difficulty":"easy","question":"In ASA congruence, how many angles are compared?","options":{"A":"1","B":"2","C":"3","D":"0"},"correct_answer":"B"},
    {"id":104,"difficulty":"easy","question":"Which congruence rule fails if the included angle is not known?","options":{"A":"SSS","B":"ASA","C":"SAS","D":"RHS"},"correct_answer":"C"},
    {"id":105,"difficulty":"easy","question":"Which criterion guarantees triangle congruence without measuring angles?","options":{"A":"ASA","B":"SAS","C":"SSS","D":"AAS"},"correct_answer":"C"},
    {"id":106,"difficulty":"easy","question":"If two triangles are congruent, their corresponding angles are:","options":{"A":"Unequal","B":"Equal","C":"Supplementary","D":"Complementary"},"correct_answer":"B"},
    {"id":107,"difficulty":"easy","question":"Which rule uses exactly one side and two angles?","options":{"A":"SSS","B":"SAS","C":"ASA","D":"AAA"},"correct_answer":"C"},
    {"id":108,"difficulty":"easy","question":"Which of the following is NOT sufficient to prove triangle congruence?","options":{"A":"SSS","B":"SAS","C":"ASA","D":"AAA"},"correct_answer":"D"},
    {"id":109,"difficulty":"easy","question":"In SAS congruence, the angle must be between the two given:","options":{"A":"Angles","B":"Sides","C":"Triangles","D":"Vertices"},"correct_answer":"B"},
    {"id":110,"difficulty":"easy","question":"Which congruence rule compares only side lengths?","options":{"A":"ASA","B":"SAS","C":"SSS","D":"AAS"},"correct_answer":"C"},
    {"id":111,"difficulty":"easy","question":"If two triangles satisfy SSS, their areas are:","options":{"A":"Unequal","B":"Equal","C":"Proportional","D":"Unrelated"},"correct_answer":"B"},
    {"id":112,"difficulty":"easy","question":"Which rule needs both ruler and protractor?","options":{"A":"SSS","B":"SAS","C":"ASA","D":"Only SSS"},"correct_answer":"C"},
    {"id":113,"difficulty":"easy","question":"Which congruence rule is based on three independent measurements?","options":{"A":"ASA","B":"SAS","C":"SSS","D":"AAA"},"correct_answer":"C"},
    {"id":114,"difficulty":"easy","question":"If only angles of two triangles are equal, the triangles are:","options":{"A":"Congruent","B":"Similar","C":"Right","D":"Isosceles"},"correct_answer":"B"},
    {"id":115,"difficulty":"easy","question":"Which rule uses the included side between two angles?","options":{"A":"SSS","B":"SAS","C":"ASA","D":"AAA"},"correct_answer":"C"},
    {"id":116,"difficulty":"easy","question":"Which congruence rule does NOT involve any angle?","options":{"A":"SSS","B":"SAS","C":"ASA","D":"AAS"},"correct_answer":"A"},
    {"id":117,"difficulty":"easy","question":"If triangles are congruent, their corresponding sides are:","options":{"A":"Proportional","B":"Unequal","C":"Equal","D":"Parallel"},"correct_answer":"C"},
    {"id":118,"difficulty":"easy","question":"Which criterion compares exactly three sides?","options":{"A":"ASA","B":"SAS","C":"SSS","D":"RHS"},"correct_answer":"C"},
    {"id":119,"difficulty":"easy","question":"Which rule requires the side to be between the two angles?","options":{"A":"SSS","B":"SAS","C":"ASA","D":"AAA"},"correct_answer":"C"},
    {"id":120,"difficulty":"easy","question":"Which congruence rule cannot be verified using a ruler alone?","options":{"A":"SSS","B":"SAS","C":"ASA","D":"All"},"correct_answer":"C"},

    {"id":121,"difficulty":"medium","question":"Two triangles have sides 6 cm, 8 cm and included angle 50° equal. Which rule applies?","options":{"A":"SSS","B":"ASA","C":"SAS","D":"AAA"},"correct_answer":"C"},
    {"id":122,"difficulty":"medium","question":"Two triangles have sides 5 cm, 7 cm, 9 cm each. Which criterion proves congruence?","options":{"A":"ASA","B":"SAS","C":"SSS","D":"AAS"},"correct_answer":"C"},
    {"id":123,"difficulty":"medium","question":"If two triangles have angles 45° and 65° equal and the side between them equal, they are congruent by:","options":{"A":"SAS","B":"ASA","C":"SSS","D":"AAA"},"correct_answer":"B"},
    {"id":124,"difficulty":"medium","question":"Which extra information converts SSA into a valid congruence case?","options":{"A":"Third side","B":"Right angle","C":"Area","D":"Perimeter"},"correct_answer":"B"},
    {"id":125,"difficulty":"medium","question":"Two triangles have sides 8 cm, 15 cm, 17 cm each. What rule applies?","options":{"A":"ASA","B":"SAS","C":"SSS","D":"AAA"},"correct_answer":"C"},
    {"id":126,"difficulty":"medium","question":"In ASA congruence, if two angles are 40° and 70°, the third angle is:","options":{"A":"60°","B":"70°","C":"80°","D":"90°"},"correct_answer":"C"},
    {"id":127,"difficulty":"medium","question":"Which information is insufficient to prove congruence?","options":{"A":"SSS","B":"SAS","C":"ASA","D":"AAA"},"correct_answer":"D"},
    {"id":128,"difficulty":"medium","question":"Two triangles have sides 9 cm, 12 cm, 15 cm. They are congruent because:","options":{"A":"SSS","B":"SAS","C":"ASA","D":"AAA"},"correct_answer":"A"},
    {"id":129,"difficulty":"medium","question":"In SAS, if sides are fixed, the triangle shape changes when:","options":{"A":"Angle changes","B":"Side changes","C":"Perimeter changes","D":"Nothing changes"},"correct_answer":"A"},
    {"id":130,"difficulty":"medium","question":"Which rule guarantees a unique triangle construction?","options":{"A":"AAA","B":"SSA","C":"SSS","D":"AA"},"correct_answer":"C"},

    {"id":131,"difficulty":"hard","question":"In ΔABC ≅ ΔPQR by SAS, AB = 2x+4, PQ = 16, BC = 3y-2, QR = 19. Find x+y.","options":{"A":"8","B":"9","C":"10","D":"11"},"correct_answer":"C"},
    {"id":132,"difficulty":"hard","question":"Two triangles have sides in ratio 3:4:5 and are congruent. If perimeter is 48 cm, find the longest side.","options":{"A":"16 cm","B":"18 cm","C":"20 cm","D":"24 cm"},"correct_answer":"C"},
    {"id":133,"difficulty":"hard","question":"For fixed sides a and b, the maximum third side occurs when included angle is:","options":{"A":"30°","B":"60°","C":"90°","D":"180°"},"correct_answer":"D"},
    {"id":134,"difficulty":"hard","question":"In ASA congruence, ∠A = (x+10)°, ∠B = (2x)°, ∠C = 70°. Find x.","options":{"A":"15","B":"20","C":"25","D":"30"},"correct_answer":"B"},
    {"id":135,"difficulty":"hard","question":"Two triangles have sides 10 cm, 24 cm, 26 cm. What rule applies?","options":{"A":"ASA","B":"SAS","C":"SSS","D":"AAA"},"correct_answer":"C"},
    {"id":136,"difficulty":"hard","question":"If two triangles satisfy SAS but included angles differ, the triangles are:","options":{"A":"Congruent","B":"Similar","C":"Not congruent","D":"Right"},"correct_answer":"C"},
    {"id":137,"difficulty":"hard","question":"In ΔABC ≅ ΔXYZ by ASA, AB = (x+5) cm, XY = 17 cm. Find x.","options":{"A":"10","B":"11","C":"12","D":"13"},"correct_answer":"C"},
    {"id":138,"difficulty":"hard","question":"Two right triangles have legs 9 cm and 12 cm. Which rule ensures congruence?","options":{"A":"SSS","B":"ASA","C":"SAS","D":"AAA"},"correct_answer":"C"},
    {"id":139,"difficulty":"hard","question":"If two triangles have equal sides but different included angles, they are:","options":{"A":"Always congruent","B":"Sometimes congruent","C":"Never congruent","D":"Always similar"},"correct_answer":"C"},
    {"id":140,"difficulty":"hard","question":"In ΔABC ≅ ΔPQR by SSS, sides are 7 cm, 24 cm, 25 cm. What type of triangle is it?","options":{"A":"Acute","B":"Obtuse","C":"Right","D":"Equilateral"},"correct_answer":"C"},
    {"id":141,"difficulty":"hard","question":"Two triangles have sides 6 cm, 8 cm and included angle 90°. Find third side.","options":{"A":"8 cm","B":"10 cm","C":"12 cm","D":"14 cm"},"correct_answer":"B"},
    {"id":142,"difficulty":"hard","question":"Which case does NOT ensure unique triangle formation?","options":{"A":"SSS","B":"SAS","C":"ASA","D":"SSA"},"correct_answer":"D"},
    {"id":143,"difficulty":"hard","question":"If two triangles are congruent by SSS, changing one angle will make them:","options":{"A":"Still congruent","B":"Similar","C":"Not congruent","D":"Right"},"correct_answer":"C"},
    {"id":144,"difficulty":"hard","question":"Two equilateral triangles have side ratio 3:5. Area ratio is:","options":{"A":"3:5","B":"9:25","C":"5:3","D":"25:9"},"correct_answer":"B"},
    {"id":145,"difficulty":"hard","question":"In ΔABC ≅ ΔDEF by SAS, AB = 10 cm, BC = 6 cm, ∠B = 90°. Find AC.","options":{"A":"8 cm","B":"10 cm","C":"12 cm","D":"14 cm"},"correct_answer":"C"},
    {"id":146,"difficulty":"hard","question":"If two triangles have equal perimeters and satisfy SAS, they are:","options":{"A":"Always congruent","B":"Sometimes congruent","C":"Never congruent","D":"Similar"},"correct_answer":"A"},
    {"id":147,"difficulty":"hard","question":"In ASA congruence, if angles are 50° and 60°, third angle is:","options":{"A":"60°","B":"70°","C":"80°","D":"90°"},"correct_answer":"C"},
    {"id":148,"difficulty":"hard","question":"Two triangles with sides 5 cm, 5 cm, 7 cm and 5 cm, 5 cm, 9 cm are:","options":{"A":"Congruent","B":"Similar","C":"Not congruent","D":"Right"},"correct_answer":"C"},
    {"id":149,"difficulty":"hard","question":"In ΔPQR ≅ ΔXYZ by SAS, PQ = 12 cm, QR = 5 cm, ∠Q = 90°. Find PR.","options":{"A":"13 cm","B":"15 cm","C":"17 cm","D":"19 cm"},"correct_answer":"A"},
    {"id":150,"difficulty":"hard","question":"Which set of information always proves triangle congruence?","options":{"A":"AAA","B":"SSA","C":"SSS","D":"AA"},"correct_answer":"C"}
,
   {"id":101,"difficulty":"easy","question":"Which congruence rule uses two sides and the angle between them?","options":{"A":"SSS","B":"ASA","C":"SAS","D":"AAA"},"correct_answer":"C"},
    {"id":102,"difficulty":"easy","question":"If three sides of one triangle are equal to three sides of another, the triangles are congruent by:","options":{"A":"ASA","B":"SAS","C":"SSS","D":"AAS"},"correct_answer":"C"},
    {"id":103,"difficulty":"easy","question":"In ASA congruence, how many angles are compared?","options":{"A":"1","B":"2","C":"3","D":"0"},"correct_answer":"B"},
    {"id":104,"difficulty":"easy","question":"Which congruence rule fails if the included angle is not known?","options":{"A":"SSS","B":"ASA","C":"SAS","D":"RHS"},"correct_answer":"C"},
    {"id":105,"difficulty":"easy","question":"Which criterion guarantees triangle congruence without measuring angles?","options":{"A":"ASA","B":"SAS","C":"SSS","D":"AAS"},"correct_answer":"C"},
    {"id":106,"difficulty":"easy","question":"If two triangles are congruent, their corresponding angles are:","options":{"A":"Unequal","B":"Equal","C":"Supplementary","D":"Complementary"},"correct_answer":"B"},
    {"id":107,"difficulty":"easy","question":"Which rule uses exactly one side and two angles?","options":{"A":"SSS","B":"SAS","C":"ASA","D":"AAA"},"correct_answer":"C"},
    {"id":108,"difficulty":"easy","question":"Which of the following is NOT sufficient to prove triangle congruence?","options":{"A":"SSS","B":"SAS","C":"ASA","D":"AAA"},"correct_answer":"D"},
    {"id":109,"difficulty":"easy","question":"In SAS congruence, the angle must be between the two given:","options":{"A":"Angles","B":"Sides","C":"Triangles","D":"Vertices"},"correct_answer":"B"},
    {"id":110,"difficulty":"easy","question":"Which congruence rule compares only side lengths?","options":{"A":"ASA","B":"SAS","C":"SSS","D":"AAS"},"correct_answer":"C"},
    {"id":111,"difficulty":"easy","question":"If two triangles satisfy SSS, their areas are:","options":{"A":"Unequal","B":"Equal","C":"Proportional","D":"Unrelated"},"correct_answer":"B"},
    {"id":112,"difficulty":"easy","question":"Which rule needs both ruler and protractor?","options":{"A":"SSS","B":"SAS","C":"ASA","D":"Only SSS"},"correct_answer":"C"},
    {"id":113,"difficulty":"easy","question":"Which congruence rule is based on three independent measurements?","options":{"A":"ASA","B":"SAS","C":"SSS","D":"AAA"},"correct_answer":"C"},
    {"id":114,"difficulty":"easy","question":"If only angles of two triangles are equal, the triangles are:","options":{"A":"Congruent","B":"Similar","C":"Right","D":"Isosceles"},"correct_answer":"B"},
    {"id":115,"difficulty":"easy","question":"Which rule uses the included side between two angles?","options":{"A":"SSS","B":"SAS","C":"ASA","D":"AAA"},"correct_answer":"C"},
    {"id":116,"difficulty":"easy","question":"Which congruence rule does NOT involve any angle?","options":{"A":"SSS","B":"SAS","C":"ASA","D":"AAS"},"correct_answer":"A"},
    {"id":117,"difficulty":"easy","question":"If triangles are congruent, their corresponding sides are:","options":{"A":"Proportional","B":"Unequal","C":"Equal","D":"Parallel"},"correct_answer":"C"},
    {"id":118,"difficulty":"easy","question":"Which criterion compares exactly three sides?","options":{"A":"ASA","B":"SAS","C":"SSS","D":"RHS"},"correct_answer":"C"},
    {"id":119,"difficulty":"easy","question":"Which rule requires the side to be between the two angles?","options":{"A":"SSS","B":"SAS","C":"ASA","D":"AAA"},"correct_answer":"C"},
    {"id":120,"difficulty":"easy","question":"Which congruence rule cannot be verified using a ruler alone?","options":{"A":"SSS","B":"SAS","C":"ASA","D":"All"},"correct_answer":"C"},

    {"id":121,"difficulty":"medium","question":"Two triangles have sides 6 cm, 8 cm and included angle 50° equal. Which rule applies?","options":{"A":"SSS","B":"ASA","C":"SAS","D":"AAA"},"correct_answer":"C"},
    {"id":122,"difficulty":"medium","question":"Two triangles have sides 5 cm, 7 cm, 9 cm each. Which criterion proves congruence?","options":{"A":"ASA","B":"SAS","C":"SSS","D":"AAS"},"correct_answer":"C"},
    {"id":123,"difficulty":"medium","question":"If two triangles have angles 45° and 65° equal and the side between them equal, they are congruent by:","options":{"A":"SAS","B":"ASA","C":"SSS","D":"AAA"},"correct_answer":"B"},
    {"id":124,"difficulty":"medium","question":"Which extra information converts SSA into a valid congruence case?","options":{"A":"Third side","B":"Right angle","C":"Area","D":"Perimeter"},"correct_answer":"B"},
    {"id":125,"difficulty":"medium","question":"Two triangles have sides 8 cm, 15 cm, 17 cm each. What rule applies?","options":{"A":"ASA","B":"SAS","C":"SSS","D":"AAA"},"correct_answer":"C"},
    {"id":126,"difficulty":"medium","question":"In ASA congruence, if two angles are 40° and 70°, the third angle is:","options":{"A":"60°","B":"70°","C":"80°","D":"90°"},"correct_answer":"C"},
    {"id":127,"difficulty":"medium","question":"Which information is insufficient to prove congruence?","options":{"A":"SSS","B":"SAS","C":"ASA","D":"AAA"},"correct_answer":"D"},
    {"id":128,"difficulty":"medium","question":"Two triangles have sides 9 cm, 12 cm, 15 cm. They are congruent because:","options":{"A":"SSS","B":"SAS","C":"ASA","D":"AAA"},"correct_answer":"A"},
    {"id":129,"difficulty":"medium","question":"In SAS, if sides are fixed, the triangle shape changes when:","options":{"A":"Angle changes","B":"Side changes","C":"Perimeter changes","D":"Nothing changes"},"correct_answer":"A"},
    {"id":130,"difficulty":"medium","question":"Which rule guarantees a unique triangle construction?","options":{"A":"AAA","B":"SSA","C":"SSS","D":"AA"},"correct_answer":"C"},

    {"id":131,"difficulty":"hard","question":"In ΔABC ≅ ΔPQR by SAS, AB = 2x+4, PQ = 16, BC = 3y-2, QR = 19. Find x+y.","options":{"A":"8","B":"9","C":"10","D":"11"},"correct_answer":"C"},
    {"id":132,"difficulty":"hard","question":"Two triangles have sides in ratio 3:4:5 and are congruent. If perimeter is 48 cm, find the longest side.","options":{"A":"16 cm","B":"18 cm","C":"20 cm","D":"24 cm"},"correct_answer":"C"},
    {"id":133,"difficulty":"hard","question":"For fixed sides a and b, the maximum third side occurs when included angle is:","options":{"A":"30°","B":"60°","C":"90°","D":"180°"},"correct_answer":"D"},
    {"id":134,"difficulty":"hard","question":"In ASA congruence, ∠A = (x+10)°, ∠B = (2x)°, ∠C = 70°. Find x.","options":{"A":"15","B":"20","C":"25","D":"30"},"correct_answer":"B"},
    {"id":135,"difficulty":"hard","question":"Two triangles have sides 10 cm, 24 cm, 26 cm. What rule applies?","options":{"A":"ASA","B":"SAS","C":"SSS","D":"AAA"},"correct_answer":"C"},
    {"id":136,"difficulty":"hard","question":"If two triangles satisfy SAS but included angles differ, the triangles are:","options":{"A":"Congruent","B":"Similar","C":"Not congruent","D":"Right"},"correct_answer":"C"},
    {"id":137,"difficulty":"hard","question":"In ΔABC ≅ ΔXYZ by ASA, AB = (x+5) cm, XY = 17 cm. Find x.","options":{"A":"10","B":"11","C":"12","D":"13"},"correct_answer":"C"},
    {"id":138,"difficulty":"hard","question":"Two right triangles have legs 9 cm and 12 cm. Which rule ensures congruence?","options":{"A":"SSS","B":"ASA","C":"SAS","D":"AAA"},"correct_answer":"C"},
    {"id":139,"difficulty":"hard","question":"If two triangles have equal sides but different included angles, they are:","options":{"A":"Always congruent","B":"Sometimes congruent","C":"Never congruent","D":"Always similar"},"correct_answer":"C"},
    {"id":140,"difficulty":"hard","question":"In ΔABC ≅ ΔPQR by SSS, sides are 7 cm, 24 cm, 25 cm. What type of triangle is it?","options":{"A":"Acute","B":"Obtuse","C":"Right","D":"Equilateral"},"correct_answer":"C"},
    {"id":141,"difficulty":"hard","question":"Two triangles have sides 6 cm, 8 cm and included angle 90°. Find third side.","options":{"A":"8 cm","B":"10 cm","C":"12 cm","D":"14 cm"},"correct_answer":"B"},
    {"id":142,"difficulty":"hard","question":"Which case does NOT ensure unique triangle formation?","options":{"A":"SSS","B":"SAS","C":"ASA","D":"SSA"},"correct_answer":"D"},
    {"id":143,"difficulty":"hard","question":"If two triangles are congruent by SSS, changing one angle will make them:","options":{"A":"Still congruent","B":"Similar","C":"Not congruent","D":"Right"},"correct_answer":"C"},
    {"id":144,"difficulty":"hard","question":"Two equilateral triangles have side ratio 3:5. Area ratio is:","options":{"A":"3:5","B":"9:25","C":"5:3","D":"25:9"},"correct_answer":"B"},
    {"id":145,"difficulty":"hard","question":"In ΔABC ≅ ΔDEF by SAS, AB = 10 cm, BC = 6 cm, ∠B = 90°. Find AC.","options":{"A":"8 cm","B":"10 cm","C":"12 cm","D":"14 cm"},"correct_answer":"C"},
    {"id":146,"difficulty":"hard","question":"If two triangles have equal perimeters and satisfy SAS, they are:","options":{"A":"Always congruent","B":"Sometimes congruent","C":"Never congruent","D":"Similar"},"correct_answer":"A"},
    {"id":147,"difficulty":"hard","question":"In ASA congruence, if angles are 50° and 60°, third angle is:","options":{"A":"60°","B":"70°","C":"80°","D":"90°"},"correct_answer":"C"},
    {"id":148,"difficulty":"hard","question":"Two triangles with sides 5 cm, 5 cm, 7 cm and 5 cm, 5 cm, 9 cm are:","options":{"A":"Congruent","B":"Similar","C":"Not congruent","D":"Right"},"correct_answer":"C"},
    {"id":149,"difficulty":"hard","question":"In ΔPQR ≅ ΔXYZ by SAS, PQ = 12 cm, QR = 5 cm, ∠Q = 90°. Find PR.","options":{"A":"13 cm","B":"15 cm","C":"17 cm","D":"19 cm"},"correct_answer":"A"},
    {"id":150,"difficulty":"hard","question":"Which set of information always proves triangle congruence?","options":{"A":"AAA","B":"SSA","C":"SSS","D":"AA"},"correct_answer":"C"}


]
}