question about postulates and theorems

[cloudvslink91]

Hey I'm having a little trouble. I don't seem to understand what exactly makes the SSS, ASA, and SAS postulates and what makes the HL and AAS theorems. Any help would be greatly appreciated.

Thanks in advance.

 

[jonboy]

a google search would probably lead you to your destination.

 

[Deleted member 4993]

Hey I'm having a little trouble. I don't seem to understand what exactly makes the SSS, ASA, and SAS postulates and what makes the HL and AAS theorems. Any help would be greatly appreciated.

Thanks in advance.

Postulates are given truth - for example "the shortest distance between two points is a straight line".

Another famous postulate (Euclid's Fifth) - "Given a line and a point outside the line - there can be only one line parallel to the given line, through the given point." Actually, this is a corollary from his actual postulate - which is kind of complicated.

Anyways, in my days of school - all these were "theorems" (SSS, ASA & SAS) - derivable from postulates and proven theorems ahead of those. For example, SAS is Euclid's proposition (theorem) #4 .

 

[Loren]

SSS: If two triangles have their three sides respectively equal to each other, then the triangles are congruent.

ASA: If two angles and the included side of one triangle are respectively equal to two angles and the included side of another triangle, then the two triangles are congruent.

SAS: If two sides and the included angle of one triangle are respectively equal to two sides and the included angle of another triangle, then the two triangles are congruent.

I don't know what HL means. But AAS is easily deduced from ASA in that If two angles of a triangle are equal to two angles of another triangle then the third angles are equal. And with all three angles respectively equal any included side gives ASA.

 

[pka]

I don't seem to understand what exactly makes the SSS, ASA, and SAS postulates and what makes the HL and AAS theorems.

It is pointless to try to answer this question absent knowing exactly what axiom set the question is based upon. There are several different sets of axioms. Each takes a different set of the above as axioms and derives the others as theorems.

 

[tkhunny]

I don't know what HL means.

HL is a non-ambiguous case of SSA for Right Triangles.