Name the inequality theorem that supports the statement.? Can anyone help?

Question

I've posted this like twice, it seems no one knows the answer!

http://tinypic.com/view.php?pic=4yty33n&s=1

1. m angleTRS > m angle WUV

2. DE > AB

3. m angle 1 > m angle 2

I don't know what 1 is, but i think 2 is sas, and 3 is corresponding. HELP?

Answer 1

The 1st cannot be answered because there is insuuficient data. You need to indicate that TS >12.

In problem 2 you do not label the triangle. But the theorem would be "if two triangles have two sides of one = to 2 sides of the other, and the included angle of one is greater than the included angle of the other, then the side opposite the larger angle will be greater than the side opposite the smaller angle.

The 3rd problem is similar to the 2nd problem. The theorem is the converse of the theorem stated in problem 2. Since 5>4, angle 1 > angle 2. Each triangle has two sides of one = to two sides of the other and the side opposite the included angles of one is greater than the side opposite, the included angle of the other, so angle opposit larger side igreater than angle opposite smaller side.

You can think of it as SAS where the two A's are not equal and hence the two triangle cannot be congruent and thus their 3rd sides cannot be equal. Euclid has proved that the the side opposite the larger angle will be greater than the side opposite the smaller angle.

Answer 2

They are all illustrating the following theorems:
(A) If two triangles have two sides that are congruent, the triangle with the larger third side will have a larger included angle.

(B) If two triangles have two sides that are congruent, the triangle with the larger included angle will have a larger third side.

Thus,
1. Since m angle TRS > m angle WUV, then by (B), side ST > side VW, or, side ST > 12.
2. I'm guessing DE is the side opposite the 39 degree angle, and AB is the side opposite the 38 degree angle (since the triangles are not labeled and would not make sense otherwise). So this is true by (B) also.
3. This diagram still follows the same ideas, because there are two triangles with two congruent sides (one side is shared between the two triangles). Therefore, m angle 1 > m angle 2 must be false based on (A). Since 4 < 5, then the angles opposite must behave the same, so m angle 1 < m angle 2.
I'm not sure if this is what you are looking for, but it's hard to tell with the diagram lacking info. Hope this helps some. Good luck.