Question

Okay, here is another one of my famous homework questions. :)

Answer 1

Very famous?

Answer 2

Yes, that'd be part of your approach. I noticed immediately that these are right triangles, in that both have a 90 degreeangle. agreed?

Answer 3

Where would you begin?

Answer 4

Here, use the name of the part of the triangle instead of "it." too vague. ;(

Answer 5

just a sec.

Answer 6

Beautiful. In fact, you're ahead of me in noticing that the smaller triangle is not isosceles.

Answer 7

Now we need to use that info to determine how much larger the larger triangle is. We did something like that before, in another problem. Strictly speaking, just writing a ratio of side lengths should be sufficient.

Answer 8

The question I'm trying to settle for myself is: " Are these two triangles similar?" What does "similar" mean in this context?

Answer 9

Only that the angles are the same, sofia. A quick look at our two triangles reveals that the sizes are different, but that the corresponding angles could be the same.

Answer 10

The two vertical sides do seem to be parallel, altho I can't yet prove it. So, what I'm proposing is that we ASSUME that the two triangles are similar, meaning (again) that their corresponding angles are equal.

Answer 11

Next, rotate the entire smaller triangle so that it nests within the larger one: