1. ## Triangle inequality challenge

I am supposed to do this without using the Pythagorean Triples because we're not up to that chapter yet. The back of my text says that Angle 2 is greater than Angle X. Help is much appreciated!

2. ## Re: Triangle inequality challenge

Originally Posted by lamp23

I am supposed to do this without using the Pythagorean Triples because we're not up to that chapter yet. The back of my text says that Angle 2 is greater than Angle X. Help is much appreciated!
I not sure what is expected of you in terms of reasoning.
There is a theorem that says: In a triangle the measure of corresponds to the measure of the opposite side. In other words, the longest side is opposite the largest angle.

3. ## Re: Triangle inequality challenge

Originally Posted by Plato
I not sure what is expected of you in terms of reasoning.
There is a theorem that says: In a triangle the measure of corresponds to the measure of the opposite side. In other words, the longest side is opposite the largest angle.
I am given that and the converse and I know how to use that on each individual triangle but I do not know how to figure out that Angle 2 is greater than Angle X because they are not in the same triangle.

4. ## Re: Triangle inequality challenge

Originally Posted by lamp23
I am given that and the converse and I know how to use that on each individual triangle but I do not know how to figure out that Angle 2 is greater than Angle X because they are not in the same triangle.
$\displaystyle m(\angle 2) = m(\angle X) + m(\angle XZW)>m(\angle X)$

WHY is that the case?

5. ## Re: Triangle inequality challenge

Originally Posted by Plato
$\displaystyle m(\angle 2) = m(\angle X) + m(\angle XZW)>m(\angle X)$

WHY is that the case?
The exterior angle theorem. Thanks!