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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]
Using this reasoning we can tell that similar triangles have congruent angles. Now, because this article is practically over, you might want to know what AA postulate can be used for. It is used proving the Angle Bisector Theorem. AA postulate is one of the many similarity ways for determining similarity in a triangle.
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The hinge theorem holds in Euclidean spaces and more generally in simply connected non-positively curved space forms.. It can be also extended from plane Euclidean geometry to higher dimension Euclidean spaces (e.g., to tetrahedra and more generally to simplices), as has been done for orthocentric tetrahedra (i.e., tetrahedra in which altitudes are concurrent) [2] and more generally for ...
Various methods may be used in practice, depending on what is known about the triangle. Other frequently used formulas for the area of a triangle use trigonometry, side lengths (Heron's formula), vectors, coordinates, line integrals, Pick's theorem, or other properties. [3]
If A lies upon a and at the same time upon another line b, we make use also of the expression: "The lines a and b have the point A in common", etc. For every two points there exists no more than one line that contains them both; consequently, if AB = a and AC = a, where B ≠ C, then also BC = a. There exist at least two points on a line.
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.
The use of the Pythagorean theorem and the tangent secant theorem can be replaced by a single application of the power of a point theorem. Case of acute angle γ , where a < 2 b cos γ . Drop the perpendicular from A onto a = BC , creating a line segment of length b cos γ .