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A theorem is a statement which is not self-evident but has been proven to be true using deductive reasoning. Many theorems come in the form of conditional statements — if-then statements that combine a hypothesis and a conclusion.
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If a triangle has a right angle, then the hypotenuse squared equals the sum of the squares of the legs. |
Sometimes, when the converse of a conditional statement is also true, the theorem is said to be a biconditional statement.
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In a coordinate plane, two non-vertical lines are perpendicular if and only if their slopes are negative reciprocals. |
Proofs of theorems are based on definitions, axioms, corollaries, or other theorems. Therefore, theorems can be used as reasons to justify statements in the proofs of other theorems.