Introduction:
An axiom is a statement that is simply accepted as being true. We have accepted the following statements as facts:
1. Alternate angles are equal. That is:
aº = bº
2. Corresponding angles are equal. That is:
bº = cº
3. The sum of adjacent angles forming a straight line is equal to 180º. That is:
aº + bº = 180º
In deductive geometry, we do not accept any other geometrical statement as being true unless it can be proved (or deduced) from the axioms.
A statement that is proved by a sequence of logical steps is called a theorem.
To prove a theorem we start by using one or more of the axioms in a particular situation to get some true statements. We then have to apply logical reasoning to these statements to produce new statements that are true. The proof ends when we arrive at the statement of the theorem.
Properties of Equality
The relation of equality has the following properties. We will use these properties in the proofs of some theorems.
1. Transitive Property
If a = b and b = c, then a = c.
2. Substitution Property
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