1. ## Inequality theorem

There are 2 questions attached.
Name the inequality theorems that supports these statements.

2. Originally Posted by Amy
There are 2 questions attached.
Name the inequality theorems that supports these statements.

I don't know if its what you are looking for but the cosine rule is sufficient
justification for these.

RonL

3. Originally Posted by CaptainBlack
I don't know if its what you are looking for but the cosine rule is sufficient
justification for these.

RonL
It is not the cosine rule. It is something else.

4. For problem 1, are you looking for something like this?

The triangles are congruent if sides TS = WV. In that case the angles TRS and WUV are equal. However TS > WV so we may say that angle TRS is greater than WUV.

It works, but I don't like this argument for the following reasons:
1) It rests on the requirement that angles stay the same as we go from one triangle to another and there is no a priori reason to assume this.

2) The proof of this argument is likely going to rely on using the Law of Cosines, as CaptainBlack suggested.

So I agree with CaptainBlack's comment.

-Dan

5. I google searched it and found it like this.

INEQUALITIES IN TWO TRIANGLES

THEOREM : SSS INEQUALITY THEOREM: In two triangles with two sides congruent, but the third sides not congruent, then the smaller included angle is opposite the smaller side.
THEOREM : SAS INEQUALITY THEOREM: In two triangles with two sides congruent but included angles not congruent, then the third sides are not congruent, and the smaller side is opposite the smaller included angle.

So here, first is SSS INEQUALITY THEOREM
and
Second is SAS INEQUALITY THEOREM.