An axiom is a statement that is taken to be true without proof^{[1]}. An axiom is taken to be self-evidently true, or obviously true. In contrast, a conjecture and a hypothesis are believed to be true, but are not self-evident.
In math, all proofs start directly or indirectly with one or more axioms. The word postulate means the same thing as axiom. An axiomatic system is a logical system that is based on axioms.
Name | Representation | Description |
---|---|---|
Betweenness Assumption | Given
collinear
points A, B, and C, C is between
A and B if AC + CB = AB.
Click on the blue points in manipulative 1 and drag them to change the figure. Notice that if C is between A and B that AC + CB = AB. If C is not between A and B then AC + CB > AB. | |
Angle Addition Postulate |
If two angles are
adjacent,
they can be added together to form a larger angle. The measure of the larger angle
is the sum of the measures of the two smaller angles.
Click on the blue points in manipulative 2 and drag them to change the figure. Notice that m∠BAC + m∠CAD = m∠BAD. | |
Table 1: Examples of axioms |
# | A | B | C | D |
E | F | G | H | I |
J | K | L | M | N |
O | P | Q | R | S |
T | U | V | W | X |
Y | Z |
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