A theorem is something you can prove, based on your postulates.Įvidently Alona’s textbook calls these postulates, while Doctor Jubal’s calls them theorems. A postulate is something you just state and assume to be true. But Alona is probably referring specifically to this page from 2001: AAA, ASS, SSA TheoremsĬan you please tell me in detail why the ASS, SSA, and AAA postulates can't be used to determine triangle congruence?ĭoctor Jubal started his answer by saying, Just a side note: the SSS, SAS, and ASA triangle congruency theorems are theorems, not postulates. Do the words "theorem" or "postulate" really matter? I am a high school student studying geometry right now and your answers to my questions would be a great help for me.īelow, we’ll be looking at one of the earlier answers referred to here. But, why do books and even teachers still teach students like us SSS, SAS, and AAS "POSTULATES". Sorry, I know you've answered questions about the topic many times but as I was reading the answers I realized that you were trying to say that SSS, SAS, and AAS are really theorems because they were proved (theorems need proofs). If SSS, SAS, and AAS are theorems, why do other books still use them as postulates? And can you show me the PROOFS that were used for these theorems? :) First, from 2006: Theorems and Postulates We’ll first look at a simple version of the question, and then one that takes us deeply into geometry. Often, this question is mixed together with a different question: Why do different texts give different lists of postulates, so that what one calls a postulate, another calls a theorem? How can we live in a mathematical world where the very foundations keep changing? My book calls them postulates To learn more about how we help parents and students in Vancouver visit: Tutoring in Vancouver.Last time we looked at the question of why we have to have postulates, which are not proved, rather than being able to prove everything. We offer tutoring programs for students in K-12, AP classes, and college. SchoolTutoring Academy is the premier educational services company for K-12 and college students. If two sides and the included angle (angle between these two sides) of one triangle are congruent to the corresponding two sides and the included angle of a second triangle, then the two triangles are congruent. Side-Angle-Side Postulate (SAS postulate) If all three sides of a triangle are congruent to corresponding three sides of other triangle then the two triangles are congruent.Īngle-Side-Angle Postulate (ASA postulate)Īccording to this postulate the two triangles are said to be congruent if two angles and the side between these two angles of one triangle are congruent to corresponding angles and the included side (side between two angles) of the other triangle. If the hypotenuse and one of the legs (sides) of a right triangle are congruent to hypotenuse and corresponding leg of the other right triangle, the two triangles are said to be congruent. There are two theorems and three postulates that are used to identify congruent triangles.Īs per this theorem the two triangles are congruent if two angles and a side not between these two angles of one triangle are congruent to two corresponding angles and the corresponding side not between the angles of the other triangle. When triangles are congruent corresponding sides (sides in same position) and corresponding angles (angles in same position) are congruent (equal). Two triangles are said to be congruent if they have same shape and same size.
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