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  2. Converse relation - Wikipedia

    en.wikipedia.org/wiki/Converse_relation

    In the monoid of binary endorelations on a set (with the binary operation on relations being the composition of relations), the converse relation does not satisfy the definition of an inverse from group theory, that is, if is an arbitrary relation on , then does not equal the identity relation on in general.

  3. Contraposition - Wikipedia

    en.wikipedia.org/wiki/Contraposition

    The converse is "If a polygon has four sides, then it is a quadrilateral. " Again, in this case, unlike the last example, the converse of the statement is true. The negation is " There is at least one quadrilateral that does not have four sides.

  4. Converse (logic) - Wikipedia

    en.wikipedia.org/wiki/Converse_(logic)

    In logic and mathematics, the converse of a categorical or implicational statement is the result of reversing its two constituent statements. For the implication P → Q, the converse is Q → P. For the categorical proposition All S are P, the converse is All P are S. Either way, the truth of the converse is generally independent from that of ...

  5. Midpoint theorem (triangle) - Wikipedia

    en.wikipedia.org/wiki/Midpoint_theorem_(triangle)

    The converse of the theorem is true as well. That is if a line is drawn through the midpoint of triangle side parallel to another triangle side then the line will bisect the third side of the triangle. The triangle formed by the three parallel lines through the three midpoints of sides of a triangle is called its medial triangle.

  6. Menelaus's theorem - Wikipedia

    en.wikipedia.org/wiki/Menelaus's_theorem

    In Euclidean geometry, Menelaus's theorem, named for Menelaus of Alexandria, is a proposition about triangles in plane geometry. Suppose we have a triangle ABC, and a transversal line that crosses BC, AC, AB at points D, E, F respectively, with D, E, F distinct from A, B, C. A weak version of the theorem states that

  7. Intersecting chords theorem - Wikipedia

    en.wikipedia.org/wiki/Intersecting_chords_theorem

    In Euclidean geometry, the intersecting chords theorem, or just the chord theorem, is a statement that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal. It is Proposition 35 of Book 3 of Euclid's Elements.

  8. Parallel postulate - Wikipedia

    en.wikipedia.org/wiki/Parallel_postulate

    If the sum of the interior angles α and β is less than 180°, the two straight lines, produced indefinitely, meet on that side. In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's Elements, is a distinctive axiom in Euclidean geometry. It states that, in two-dimensional geometry:

  9. Glossary of algebraic geometry - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_algebraic_geometry

    These immersions are immersions in the sense above, but the converse is false. Furthermore, under this definition, the composite of two immersions is not necessarily an immersion. However, the two definitions are equivalent when f is quasi-compact. [16]