Ratios in a right-angled triangle

If we divide the hypotenuse of a right-angled triangle, by drawing a perpendicular to the opposite vertex, then we get three similar triangles.

Considering the ratio of the sides of these triangles gives us the three results shown below.

(You may like to consider what you would see if you added a2 to b2.)

To download this Geogebra file click here.