AA postulate

AA postulate

The AA Postulate in Euclidean geometry states that two triangles are similar if they have two corresponding angles congruent.

The AA Postulate works because the interior angles of a triangle are always equal to 180°. By knowing two angles, such as 32° and 64° degrees, we know that the next angle is 84°, because 180-(32+64)=84.

(Some people refer to this as the AAA Postulate, which is true in all respects, but you truly only need two angles.) We can help to understand the postulate by working in reverse order. We can start with two triangles on grids A and B which are similar, by a 1.5 dilation from A to B. If we line up the two triangles, such as in C, we find that the angle on the origin is congruent with the other one (D). We also know that the pair of sides opposite the origin are parallel. We know this because the pairs of sides around them are similar, stem from the same point, and line up with each other. We can then look at the sides around the parallels as transversals, and therefore the corresponding angles are congruent. Using this reasoning we can tell that similar triangles have congruent angles.


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  • Postulate — Pos tu*late, n. [L. postulatum a demand, request, prop. p. p. of postulare to demand, prob. a dim. of poscere to demand, prob. for porcscere; akin to G. forschen to search, investigate, Skr. prach to ask, and L. precari to pray: cf. F. postulat.… …   The Collaborative International Dictionary of English

  • Postulate — Pos tu*late, v. t. [imp. & p. p. {Postulated}; p. pr. & vb. n. {Postulating}.] 1. To beg, or assume without proof; as, to postulate conclusions. [1913 Webster] 2. To take without express consent; to assume. [1913 Webster] The Byzantine emperors… …   The Collaborative International Dictionary of English

  • postulate# — postulate vb *presuppose, presume, assume, premise, posit Analogous words: affirm, aver, predicate, *assert postulate n presupposition, presumption, assumption, premise, posit (see under PRESUPPOSE) Analogous words: *principle, axiom, theorem,… …   New Dictionary of Synonyms

  • Postulate — Pos tu*late, a. Postulated. [Obs.] Hudibras. [1913 Webster] …   The Collaborative International Dictionary of English

  • postulate — I noun assertion, assumed truth, assumption, axiom, conjecture, foundation, hypothesis, premise, speculation, starting point, statement, suggestion, sumptio, supposal, supposition, surmise, theorem, thesis, truism II verb advance, assume,… …   Law dictionary

  • postulate of reason — index principle (axiom) Burton s Legal Thesaurus. William C. Burton. 2006 …   Law dictionary

  • postulate — (v.) early 15c. (implied in postulation), nominate to a church office, from M.L. postulatus, pp. of postulare to ask, demand, probably formed from pp. of L. poscere ask urgently, demand, from *posk to , Italic inchoative of PIE root *prek to ask… …   Etymology dictionary

  • postulate — [v] suppose, figure advance, affirm, assert, assume, aver, estimate, guess, hypothesize, posit, predicate, premise, presuppose, propose, put forward, speculate, suppose, take for granted, theorize; concepts 12,26 Ant. calculate …   New thesaurus

  • postulate — ► VERB 1) suggest or assume the existence, fact, or truth of (something) as a basis for reasoning or belief. 2) nominate or elect to an ecclesiastical office subject to the sanction of a higher authority. ► NOUN ▪ a thing postulated. DERIVATIVES… …   English terms dictionary

  • postulate — [päs′chə lāt΄; ] for n., usually [, päs′chəlit] vt. postulated, postulating [< L postulatus, pp. of postulare, to demand < base of poscere, to demand < IE * pṛk̑skā, question < base * perk̑ , to ask > Ger frage, question] 1. to… …   English World dictionary

  • postulate — I n. (formal) a postulate that + clause (his postulate that the area was uninhabited proved to be true) II v. (formal) (L) they postulated that the collision had been caused by fog * * * [ pɒstjʊleɪt] (formal) (L) they postulated that the… …   Combinatory dictionary

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