{
  "title": "Congruence of Triangles - Grade 9 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "📐 Two triangles are congruent if they have the same...", "options": {"A": "area", "B": "shape and size", "C": "perimeter", "D": "angles only"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "🔺 The symbol for congruence is...", "options": {"A": "=", "B": "≈", "C": "≅", "D": "~"}, "correct_answer": "C"},
    {"id": 3, "difficulty": "easy", "question": "✅ If ΔABC ≅ ΔDEF, then side AB corresponds to side...", "options": {"A": "DE", "B": "EF", "C": "FD", "D": "BC"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "📏 Which congruence criterion requires three pairs of equal sides?", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "🔺 If two sides and the included angle of one triangle are equal to two sides and included angle of another, the triangles are congruent by...", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "AAA"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "✅ 'Included angle' means the angle...", "options": {"A": "between the two sides", "B": "opposite to a side", "C": "next to the triangle", "D": "largest angle"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "📐 If three angles of one triangle are equal to three angles of another, are they always congruent?", "options": {"A": "Yes", "B": "No", "C": "Sometimes", "D": "Only if right-angled"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "🔺 Which criterion is for right-angled triangles only?", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS"}, "correct_answer": "D"},
    {"id": 9, "difficulty": "easy", "question": "✅ In RHS congruence, 'H' stands for...", "options": {"A": "Height", "B": "Hypotenuse", "C": "Horizontal", "D": "Half"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "📏 If ΔPQR ≅ ΔXYZ, then ∠P is equal to...", "options": {"A": "∠X", "B": "∠Y", "C": "∠Z", "D": "∠Q"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "🔺 Congruent triangles have equal...", "options": {"A": "areas", "B": "perimeters", "C": "corresponding parts", "D": "all of the above"}, "correct_answer": "D"},
    {"id": 12, "difficulty": "easy", "question": "✅ If two triangles are congruent, how many pairs of equal parts do they have?", "options": {"A": "3", "B": "6", "C": "9", "D": "12"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "📐 Which is NOT a congruence criterion?", "options": {"A": "SSS", "B": "SAS", "C": "AAA", "D": "ASA"}, "correct_answer": "C"},
    {"id": 14, "difficulty": "easy", "question": "🔺 In ASA congruence, the side is...", "options": {"A": "included between the angles", "B": "opposite to first angle", "C": "the longest side", "D": "not important"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "✅ If two right triangles have their hypotenuses equal and one pair of legs equal, they are congruent by...", "options": {"A": "SSS", "B": "SAS", "C": "RHS", "D": "ASA"}, "correct_answer": "C"},
    {"id": 16, "difficulty": "easy", "question": "📏 For SAS congruence, the angle must be...", "options": {"A": "right angle", "B": "included", "C": "largest", "D": "acute"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "🔺 If ΔABC ≅ ΔDEF, then BC = ?", "options": {"A": "DE", "B": "EF", "C": "FD", "D": "DF"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "✅ Two triangles with all sides equal are congruent by...", "options": {"A": "AAA", "B": "SSS", "C": "SAS", "D": "ASA"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "📐 Congruent figures are always...", "options": {"A": "similar", "B": "different sizes", "C": "mirror images", "D": "rotated"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "🔺 Which criterion requires two angles and the included side?", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS"}, "correct_answer": "C"},
    {"id": 21, "difficulty": "medium", "question": "📐 In ΔABC and ΔDEF, if AB=DE, BC=EF, and ∠B=∠E, are they congruent? If yes, by which criterion?", "options": {"A": "Yes, by SSS", "B": "Yes, by SAS", "C": "No", "D": "Yes, by ASA"}, "correct_answer": "B"},
    {"id": 22, "difficulty": "medium", "question": "🔺 In triangles ΔPQR and ΔXYZ, PQ=XY, QR=YZ, and PR=XZ. They are congruent by...", "options": {"A": "SAS", "B": "ASA", "C": "SSS", "D": "RHS"}, "correct_answer": "C"},
    {"id": 23, "difficulty": "medium", "question": "✅ If two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another, the triangles are congruent by...", "options": {"A": "ASA", "B": "AAS", "C": "SAS", "D": "SSS"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "📏 In right triangles ΔABC and ΔDEF, right-angled at B and E, if AC=DF and AB=DE, they are congruent by...", "options": {"A": "RHS", "B": "SAS", "C": "ASA", "D": "SSS"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "🔺 Which additional information is needed to prove ΔABC ≅ ΔADC if AB=AD and BC=DC?", "options": {"A": "∠B = ∠D", "B": "AC is common", "C": "∠BAC = ∠DAC", "D": "None, already congruent"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "✅ In quadrilateral ABCD, if diagonal AC divides it into two congruent triangles ΔABC and ΔADC, what must be true?", "options": {"A": "AB=AD and BC=DC", "B": "∠B=∠D", "C": "Both A and B", "D": "None"}, "correct_answer": "C"},
    {"id": 27, "difficulty": "medium", "question": "📐 If ΔMNO ≅ ΔPQR, and MN=5 cm, what is PQ?", "options": {"A": "5 cm", "B": "10 cm", "C": "Not known", "D": "Depends on angle"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "🔺 To prove two triangles congruent using ASA, we need...", "options": {"A": "two angles and any side", "B": "two sides and any angle", "C": "two angles and the included side", "D": "two sides and included angle"}, "correct_answer": "C"},
    {"id": 29, "difficulty": "medium", "question": "✅ In an isosceles triangle, the altitude to the base divides the triangle into two... triangles.", "options": {"A": "similar", "B": "congruent", "C": "different", "D": "larger"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "📏 If two triangles have two pairs of equal angles and a pair of equal sides (not included), they are congruent by...", "options": {"A": "ASA", "B": "AAS", "C": "SAS", "D": "SSS"}, "correct_answer": "B"},
    {"id": 31, "difficulty": "medium", "question": "🔺 In the figure, AB=AC and AD is perpendicular to BC. Which triangles are congruent?", "options": {"A": "ΔABD and ΔACD", "B": "ΔABC and ΔADC", "C": "ΔABD and ΔABC", "D": "None"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "✅ If three sides of one triangle are equal to three sides of another, the triangles are congruent. This is...", "options": {"A": "always true", "B": "sometimes true", "C": "never true", "D": "true only for right triangles"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "📐 'Corresponding parts of congruent triangles are equal' is abbreviated as...", "options": {"A": "CPCTC", "B": "CPCT", "C": "CCP", "D": "CTCP"}, "correct_answer": "B"},
    {"id": 34, "difficulty": "medium", "question": "🔺 Which condition is sufficient to prove two right triangles congruent?", "options": {"A": "One acute angle equal", "B": "Hypotenuse and one acute angle equal", "C": "Two legs equal", "D": "Both B and C"}, "correct_answer": "D"},
    {"id": 35, "difficulty": "medium", "question": "✅ In ΔABC and ΔDEF, if ∠A=∠D, ∠B=∠E, and BC=EF, are they congruent? By which rule?", "options": {"A": "Yes, by ASA", "B": "Yes, by AAS", "C": "No", "D": "Yes, by SAS"}, "correct_answer": "B"},
    {"id": 36, "difficulty": "medium", "question": "📏 Two triangles are congruent if two angles and the side between them in one triangle are equal to the corresponding parts in the other. This is...", "options": {"A": "ASA criterion", "B": "SAS criterion", "C": "SSS criterion", "D": "RHS criterion"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "🔺 If in ΔABC and ΔPQR, AB=PQ, BC=QR, and ∠C=∠R, are they necessarily congruent?", "options": {"A": "Yes", "B": "No", "C": "Only if right-angled", "D": "Only if isosceles"}, "correct_answer": "B"},
    {"id": 38, "difficulty": "medium", "question": "✅ In an isosceles triangle, the median to the base is also the...", "options": {"A": "perpendicular bisector", "B": "angle bisector", "C": "altitude", "D": "all of these"}, "correct_answer": "D"},
    {"id": 39, "difficulty": "medium", "question": "📐 If ΔABC ≅ ΔPQR, and ∠A=50°, ∠B=60°, what is ∠R?", "options": {"A": "50°", "B": "60°", "C": "70°", "D": "80°"}, "correct_answer": "C"},
    {"id": 40, "difficulty": "medium", "question": "🔺 To prove two triangles congruent, which combination is NOT valid?", "options": {"A": "SSA", "B": "SAS", "C": "ASA", "D": "RHS"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "hard", "question": "📐 In quadrilateral ABCD, AB∥CD and AD∥BC. Which congruence criterion proves ΔABC ≅ ΔCDA?", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS"}, "correct_answer": "C"},
    {"id": 42, "difficulty": "hard", "question": "🔺 In ΔABC, AB=AC. D is the midpoint of BC. Which congruence proves AD is perpendicular to BC?", "options": {"A": "SSS", "B": "SAS", "C": "RHS", "D": "AAS"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "hard", "question": "✅ In two triangles, two sides and one diagonal are equal. Are they congruent?", "options": {"A": "Always", "B": "Never", "C": "Sometimes", "D": "Only if isosceles"}, "correct_answer": "C"},
    {"id": 44, "difficulty": "hard", "question": "📏 In ΔABC and ΔDEF, AB=DE, AC=DF, and ∠B=∠E. Are they congruent?", "options": {"A": "Yes, by SAS", "B": "Yes, by SSS", "C": "No, not necessarily", "D": "Yes, by ASA"}, "correct_answer": "C"},
    {"id": 45, "difficulty": "hard", "question": "🔺 In the figure, AD=BC and ∠BAD=∠ABC. Which additional info proves ΔABD ≅ ΔBAC?", "options": {"A": "AB is common", "B": "BD=AC", "C": "∠ABD=∠BAC", "D": "Any of these"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "hard", "question": "✅ If the bisector of an angle of a triangle also bisects the opposite side, the triangle is...", "options": {"A": "isosceles", "B": "equilateral", "C": "scalene", "D": "right-angled"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "hard", "question": "📐 In right triangle ABC, right-angled at B, if BD is perpendicular to AC, how many pairs of congruent triangles are in the figure?", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "C"},
    {"id": 48, "difficulty": "hard", "question": "🔺 If two triangles have two pairs of equal sides and the angles opposite to one pair of equal sides are equal, they are congruent by...", "options": {"A": "SSS", "B": "SAS", "C": "AAS", "D": "Not necessarily congruent"}, "correct_answer": "D"},
    {"id": 49, "difficulty": "hard", "question": "✅ In ΔABC, D and E are points on AB and AC such that AD=AE and BD=CE. Prove ΔABE ≅ ΔACD. Which criterion?", "options": {"A": "SSS", "B": "SAS", "C": "ASA", "D": "RHS"}, "correct_answer": "B"},
    {"id": 50, "difficulty": "hard", "question": "📏 In an equilateral triangle, all three altitudes are equal. This can be proved using...", "options": {"A": "congruence of triangles", "B": "Pythagoras theorem", "C": "similarity", "D": "area formula"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "hard", "question": "🔺 If in two right triangles, the hypotenuse and one side are equal, they are congruent by RHS. What does 'S' stand for?", "options": {"A": "Side", "B": "Segment", "C": "Straight", "D": "Smallest"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "hard", "question": "✅ In ΔABC, if ∠A=40°, ∠B=60°, and in ΔPQR, ∠P=40°, ∠Q=60°, and BC=QR. Are they congruent?", "options": {"A": "Yes", "B": "No", "C": "Only if AB=PQ", "D": "Cannot say"}, "correct_answer": "B"},
    {"id": 53, "difficulty": "hard", "question": "📐 Which of the following is a sufficient condition for congruence of two triangles?", "options": {"A": "Two sides and a non-included angle equal", "B": "Three angles equal", "C": "Two angles and a non-included side equal", "D": "All sides proportional"}, "correct_answer": "C"},
    {"id": 54, "difficulty": "hard", "question": "🔺 In ΔABC and ΔDEF, if AB=DE, BC=EF, and the median from A to BC equals the median from D to EF, are the triangles congruent?", "options": {"A": "Yes, always", "B": "No, never", "C": "Sometimes", "D": "Only if right-angled"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "hard", "question": "✅ If two triangles have equal areas and equal perimeters, are they congruent?", "options": {"A": "Always", "B": "Never", "C": "Sometimes", "D": "Only if right-angled"}, "correct_answer": "C"},
    {"id": 56, "difficulty": "hard", "question": "📏 In a parallelogram, the diagonals bisect each other. This is proved by congruence of which triangles?", "options": {"A": "Opposite triangles", "B": "Adjacent triangles", "C": "Triangles formed by diagonals", "D": "All triangles"}, "correct_answer": "C"},
    {"id": 57, "difficulty": "hard", "question": "🔺 In an isosceles triangle, the angles opposite equal sides are equal. This is proved by drawing the...", "options": {"A": "median", "B": "altitude", "C": "angle bisector", "D": "any of these"}, "correct_answer": "D"},
    {"id": 58, "difficulty": "hard", "question": "✅ In ΔABC, AB=AC. The bisector of ∠A meets BC at D. Which congruence proves BD=DC?", "options": {"A": "ΔABD ≅ ΔACD by SAS", "B": "ΔABD ≅ ΔACD by SSS", "C": "ΔABD ≅ ΔACD by ASA", "D": "Not congruent"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "hard", "question": "📐 If two triangles are congruent, their circumcircles have...", "options": {"A": "equal radii", "B": "different radii", "C": "no relation", "D": "depends"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "hard", "question": "✅ CPCT stands for Corresponding Parts of Congruent Triangles. After proving congruence, we use CPCT to prove...", "options": {"A": "triangles are similar", "B": "other equalities", "C": "areas are equal", "D": "perimeters are equal"}, "correct_answer": "B"}
  ]
}