Question

Are two right triangles always similar?

Answer 1

Not necessarily

Explanation:

Let's make it easy on ourselves and consider a `3-4-5` right triangle and a `5-12-13` right triangle. As you can see `3^2+4^2=5^2` and `5^2+12^2=13^2` which satisfies `a^2+b^2=c^2`:

If the two triangles are similar, their sides would match up and create the same ratio. However, as you can see `3/5!=4/12!=5/13`. Each side has a different ratio. Therefore, they don't necessarily have to be similar.

You can also say that the angles of the triangle don't necessarily have to be equal. A similar triangle requires that the angles are equal. However, the only fundamental rule regarding the angles of a triangle is that `theta_1+theta_2+theta_3=180`

In a right triangle, one of those angles is `90` degrees but the other two can be any other angle so long as they add up to `90`