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The congruence theorems side-angle-side (SAS) and side-side-side (SSS) also hold on a sphere; in addition, if two spherical triangles have an identical angle-angle-angle (AAA) sequence, they are congruent (unlike for plane triangles). [9] The plane-triangle congruence theorem angle-angle-side (AAS) does not hold for spherical triangles. [10]
Pages in category "Theorems about triangles" The following 29 pages are in this category, out of 29 total. This list may not reflect recent changes. A.
This is a list of notable theorems.Lists of theorems and similar statements include: List of algebras; List of algorithms; List of axioms; List of conjectures
In Euclidean geometry, the AA postulate states that two triangles are similar if they have two corresponding angles congruent.. The AA postulate follows from the fact that the sum of the interior angles of a triangle is always equal to 180°.
All pairs of congruent triangles are also similar, but not all pairs of similar triangles are congruent. Given two congruent triangles, all pairs of corresponding interior angles are equal in measure, and all pairs of corresponding sides have the same length. This is a total of six equalities, but three are often sufficient to prove congruence ...
Pages in category "Theorems about triangles and circles" The following 18 pages are in this category, out of 18 total. This list may not reflect recent changes. C.
Pages in category "Theorems in geometry" The following 48 pages are in this category, out of 48 total. This list may not reflect recent changes. 0–9. 2π theorem; A.
This is equivalent to the side-angle-side rule for determining that two triangles are congruent; if the angles uxz and u'x'z' are congruent (there exist congruent triangles xuz and x'u'z'), and the two pairs of incident sides are congruent (xu ≡ x'u' and xz ≡ x'z'), then the remaining pair of sides is also congruent (uz ≡ u'z').