Formal (two-column) Proofs: requesting info, advice

[IdontknowwhatImdoing]

So I suck at writing them. They're the two column things, one side for statements, the other for reasons. Plainly put, I need tips for writing them. I sometime can write one out but end up screwing up ONE line, other times I don't know the first thing to do. (this is plain geometry(or is it plane?)) To give you an idea of where I'm at, this is whats been covered so far:


SSS Postulate
SAS Postulate
ASA Postulate
AAS Postulate

LL Theorem
HL Theorem
LA Theorem
HA Theorem


Any pointers? Help, I don't want to fail. :shock:

 

[arthur ohlsten]

Re: Formal Proofs

I don't know the theorems. LL is meaningless to me.
The postulates I know. They define unique plane triangles

SSS side,side, side if 3 sides of 2 triangles are the same the triangles are identical

SAS side, angle, side if 2 sides and the included angle are the same the triangles are identical

ASA angle side ,angle if 2 angles and the included side are the same the triangles are identical

AAS angle, angle side are equal the triangles are identical

Resubmit the problem asking about the theorems and perhaps someone will answer
Arthur

 

[Mrspi]

Re: Formal Proofs

The "theorems" you refer to are special cases for proving right triangles congruent.

For example, the LL theorem says "If you have two right triangles, with the two legs of one equal to the two legs of the other, the triangles are congruent."

So...you have two right triangles, which by definition must each have a right angle (and all right angles are congruent). If the two legs of one of those triangles are congruent to the two legs of the other, then you essentially have SAS.....

HA and LA also equate to either the AAS or ASA triangle congruence postulates.

The only one which is DIFFERENT is HL....

If you have two right triangles with the hypotenuses congruent, and a corresponding leg in each triangle congruent, and you've got a right angle in each triangle, the two triangles must be congruent. This represents the SSA condition, which normally does not guarantee triangle congruence. However, if the triangles in question are right triangles, it is relatively easy to show the triangles are congruent by moving one right triangle so that the two congruent legs coincide.

Now...to use any of these postulates or theorems in a proof involving congruent triangles, you just have to find from the given information, what you can derive from the given information, or from the diagram, sufficient information to apply one of the postulates or theorems.

If you are not given any right triangles, or you can't be sure from what is given or what you can derive from the given information that you've got right triangles, you CANNOT use any of the theorems specified for right triangles, such as LL, HA, LA, or HL.