1. What is an axiom? Give one example.
2. What is the difference between an axiom and a theorem?
3. Write down Euclid's five postulates.
4. Name three undefined terms.
2. What is the difference between an axiom and a theorem?
3. Write down Euclid's five postulates.
4. Name three undefined terms.
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Answer:
1) A statement that is taken to be true, so that further reasoning can be done. It is not something we want to prove. Example: one of Euclid's axioms (over 2300 years ago!) is: "If A and B are two numbers that are the same, and C and D are also the same, A+C is the same as B+D"
2) An axiom is often a statement assumed to be true for the sake of expressing a logical sequence. They are the principal building blocks of proving statements. Axioms serve as the starting point of other mathematical statements. These statements, which are derived from axioms, are called theorems.
3) i) straight line segment may be drawn from any given point to any other.
ii) A straight line may be extended to any finite length.
iii) A circle may be described with any given point as its center and any distance as its radius.
iv) All right angles are congruent.
v) If a straight line intersects two other straight lines, and so makes the two interior angles on one side of it together less than two right angles, then the other straight lines will meet at a point if extended far enough on the side on which the angles are less than two right angles.
4) The main three undefined terms of geometry are Point, Line and Plane.