Ads
related to: geometry statements that are true
Search results
Results From The WOW.Com Content Network
Euclidean geometry is an axiomatic system, in which all theorems ("true statements") are derived from a small number of simple axioms. Until the advent of non-Euclidean geometry , these axioms were considered to be obviously true in the physical world, so that all the theorems would be equally true.
Let S be a statement of the form P implies Q (P → Q). Then the converse of S is the statement Q implies P (Q → P). In general, the truth of S says nothing about the truth of its converse, [2] unless the antecedent P and the consequent Q are logically equivalent. For example, consider the true statement "If I am a human, then I am mortal."
Absolute geometry is an extension of ordered geometry, and thus, all theorems in ordered geometry hold in absolute geometry. The converse is not true. Absolute geometry assumes the first four of Euclid's Axioms (or their equivalents), to be contrasted with affine geometry, which does not assume Euclid's third and fourth axioms. Ordered geometry ...
If a statement's inverse is true, then its converse is true (and vice versa). If a statement's inverse is false, then its converse is false (and vice versa). If a statement's negation is false, then the statement is true (and vice versa). If a statement (or its contrapositive) and the inverse (or the converse) are both true or both false, then ...
The statement A ∨ B is true if A or B (or both) are true; if both are false, the statement is false. n ≥ 4 ∨ n ≤ 2 ⇔ n ≠ 3 when n is a natural number. ⊕ ...
Geometry (from Ancient Greek ... [12] though the statement of the theorem has a long history. ... lies in with contains, and the result is an equally true theorem ...
This is not to say that the statements are logically equivalent (i.e., one can be proved from the other using only formal manipulations of logic), since, for example, when interpreted in the spherical model of elliptical geometry one statement is true and the other isn't. [14]
In geometry, two figures or objects are congruent if they have the same shape and size, ... BC and EF; and CA and FD, then the following statements are true: ...