The Elements of Geometry

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Step 1: Since C is midpoint of AB, AC = CB = AB/2 = 8/2 = 4 cm. Step 2: Since D is midpoint of BC, BD = CD = BC/2 = 4/2 = 2 cm. Step 3: AD = AC + CD = 4 + 2 = 6 cm. Answer: AD = 6 cm. (Using Euclid's

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Step 1: Apply Euclid's 1st postulate - 'A straight line can be drawn from any point to any point'. Step 2: This means exactly ONE unique line passes through two distinct points. Step 3: If we assume t

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Step 1: Circle 1 has center O, radius = 5 cm. Circle 2 has center P, radius = 4 cm, OP = 3 cm. Step 2: For intersection, check if |r₁ - r₂| < OP < r₁ + r₂. Step 3: |5 - 4| = 1, and 5 + 4 = 9. So 1 < 3

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Step 1: Given ∠AOB = 90° and ∠COD = 90°. Step 2: Apply Euclid's 4th postulate: 'All right angles are equal to one another'. Step 3: Since both ∠AOB and ∠COD are right angles (90°), they must be equal.

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Step 1: Check Pythagorean theorem: a² + b² = c² (where c is largest side). Step 2: Here, AC = 10 cm is largest. Check if AB² + BC² = AC². Step 3: 6² + 8² = 36 + 64 = 100, and 10² = 100. Step 4: Since

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Step 1: Given PQ = RS and RS = TU. Step 2: Apply Euclid's 1st axiom: 'Things which are equal to the same thing are equal to one another'. Step 3: Since PQ = RS and RS = TU, both PQ and TU are equal to

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Step 1: Draw line segment AB = 4 cm (any two points). Step 2: Using postulate 3, draw circle with center A and radius 4 cm. Step 3: Draw another circle with center B and radius 4 cm. Step 4: Let circl

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Step 1: Line segment PQ is extended using postulate 2 to form line l. Step 2: Line m intersects line l at point R. Step 3: Apply the theorem: 'Two distinct lines cannot have more than one point in com