In one right-angled triangle, the acute angle is 36 degrees, and in the other right-angled

In one right-angled triangle, the acute angle is 36 degrees, and in the other right-angled triangle, the acute angle is 54 degrees. Are these triangles similar? Why?

In the first triangle, only one acute angle is known. You can find what the second acute angle is.

Since the triangle is rectangular, and the sum of all angles is 180˚, the magnitude of the unknown acute angle is

180˚ – 90˚ – 36˚ = 54˚.

Before us is a triangle, the angles of which are equal to 90˚, 54˚ and 36˚.

Knowing that in the second triangle one acute angle is 54˚, we can conclude that its second acute angle is 36˚.

Therefore, the first and second triangles are similar.

Addition: We cannot say that they are equal, since we do not know anything about the length of the sides.