From Euclid's Elements Book 1, show that the 5th postulate is equivalent to proposition 32. "In any triangle, the sum of the three interior angles of the triangle equals two right angles
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Assume the 5th postulate is true, which states that if a straight line crossing two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if extended indefinitely, will meet on that side on which the angles Show more…
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1. Use Euclid's parallel postulate to prove the alternate interior angles theorem. That is, in Figure 1.2.3 (a), assume the line BD is parallel to the line AC. Prove that ∠BAC = ∠ABD. Figure 1.2.3. Two consequences of the parallel postulate. 2. Use Euclid's parallel postulate and the previous problem to prove that the sum of the angles of any triangle is 180°. You may find Figure 1.2.3 (b) helpful, where segment CD is parallel to segment AB. Figure 1.2.3. Two consequences of the parallel postulate.
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