Side && Angles 3

Using the table from my previous blog entry, I will answer the following questions:

1. So what does this make you think about triangles?
2. Do you have any more questions?
3. Can you make any generalizations?

With the information that I gathered using the table, it tells me that when all the sides of a triangle are increased by the same number nothing really changes because the sides stay proportional. It also tells me that even though two triangles have different sides it is possible that they can still have the same angle measurements. I also learned from Ms. Sheppard-Brick that there is a long list of triangles that involve other parts of the triangle, as I predicted in an earlier entry. Although I did figure that out myself before doing my own investigation, the table (list) is called Trigonometric Functions.
Some questions that I have are:

• What does the chart with the triangles, sides & angles show?
• How did mathematicians figure this out with out an equation?

A generalization that I can make is that if any three sides of a right triangle are increased by the same number multiple times they will continue to have the same angle measurements each time. A few more patterns that I noticed that all the numbers in the previous table are even numbers. I doubt that, that makes a difference because there are odd numbered sides that make right triangles too, and I believe if those stay proportional the angles will be the same as they started out.