1-double
2-halves
3-reduce by √2
4-not change

Kind of confused, haven't do this since high school. lol

 

What have you done so far?

Hint: Consider a triangle with sides of 1,2,3. Does it matter what units are used for those measures?

John

 

no it won't matter, is just a question in a text book..

 

You have just answered your own question.

John

 

You have just answered your own question.

John

Thanks

 

Now, the next part of learning is to try teaching. So, can you explain why it doesn't matter?

John

 

1-double
2-halves
3-reduce by √2
4-not change

Kind of confused, haven't do this since high school. lol

Assuming that the units stay the same (which seems highly probable to me), it's not difficult to figure out the answer to your question. Just draw two simple triangles (like 45-45-90 ones), one with sides of length x and another with sides of length 2x, and then measure the angles with a protractor.

Note: I know what the correct answer is, but it would be unethical for me to give it away.

 

I don't think it is a good idea to try to prove something using an example that might well be a special case. The proof should apply to any triangle.

If you have studied lines intersecting parallel lines, you might find those properties useful here.

I am assuming this a geometry class, not trigonometry, right?

John

 

I don't think it is a good idea to try to prove something using an example that might well be a special case. The proof should apply to any triangle.

I just mentioned 45-45-90 triangles as an example because they might be simpler to draw, but any triangle will work.

@jpanhalt: Are you saying that you think a 45-45-90 triangle would be a special case? I didn't think it would for this proof, but maybe I'm misunderstanding the OP.

 

I just mentioned 45-45-90 triangles as an example because they might be simpler to draw, but any triangle will work.

@jpanhalt: Are you saying that you think a 45-45-90 triangle would be a special case? I didn't think it would for this proof, but maybe I'm misunderstanding the OP.

The point is that if you choose fifteen triangles and show that it works for those fifteen triangles, you haven't proven that it will work for anything other than those fifteen triangles. You may have made a very strong case that it probably would work for all triangles, but you haven't "proven" anything.

 

The point is that if you choose fifteen triangles and show that it works for those fifteen triangles, you haven't proven that it will work for anything other than those fifteen triangles. You may have made a very strong case that it probably would work for all triangles, but you haven't "proven" anything.

Right. I wasn't recommending a way to make a proof, since I didn't think that's what the OP was talking about. I was assuming that he just wants to find the answer to an individual problem, but it would be an excellent idea to research the reasoning behind the proof as well.

 

Such triangles, in which all sides are scaled by the same value, are called similar triangles. Similar triangles retain their shape and the values of their angles at all scale factors except zero.
https://www.mathsisfun.com/geometry/triangles-similar.html

 

Hi,

Yeah, like linear magnification. If you look at a triangle through a telescope it still looks the same.
Trigonometry has a lot to do with ratios rather than absolute values.