Are two right triangles always similar?

1 Answer
May 27, 2017

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#