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ASA (angle-side-angle): If two pairs of angles of two triangles are equal in measurement, and the included sides are equal in length, then the triangles are congruent. The ASA postulate is attributed to Thales of Miletus. In most systems of axioms, the three criteria – SAS, SSS and ASA – are established as theorems.
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°. By knowing two angles, such as 32° and 64° degrees, we know that the next angle is 84°, because 180 ...
The pons asinorum in Oliver Byrne's edition of the Elements [1]. In geometry, the theorem that the angles opposite the equal sides of an isosceles triangle are themselves equal is known as the pons asinorum (/ ˈ p ɒ n z ˌ æ s ɪ ˈ n ɔːr ə m / PONZ ass-ih-NOR-əm), Latin for "bridge of asses", or more descriptively as the isosceles triangle theorem.
For example we see the image of the initial regular pentagon under a homothety of negative ratio –k, which is a similarity of ±180° angle and a positive ratio equal to k. Below the title on the right, the second image shows a similarity decomposed into a rotation and a homothety.
Congruence of triangles is determined by specifying two sides and the angle between them (SAS), two angles and the side between them (ASA) or two angles and a corresponding adjacent side (AAS). Specifying two sides and an adjacent angle (SSA), however, can yield two distinct possible triangles unless the angle specified is a right angle.
SAS Postulate: Two sides in a triangle have the same length as two sides in the other triangle, and the included angles have the same measure. ASA: Two interior angles and the side between them in a triangle have the same measure and length, respectively, as those in the other triangle. (This is the basis of surveying by triangulation.)
Ahead, we’ve rounded up 50 holy grail hyperbole examples — some are as sweet as sugar, and some will make you laugh out loud. 50 common hyperbole examples I’m so hungry, I could eat a horse.
Synthetic proofs of geometric theorems make use of auxiliary constructs (such as helping lines) and concepts such as equality of sides or angles and similarity and congruence of triangles. Examples of such proofs can be found in the articles Butterfly theorem, Angle bisector theorem, Apollonius' theorem, British flag theorem, Ceva's theorem ...