Whaddayaknow? It's the same proportion as the geometric mean. Aybeesee's height is the short side of one baby triangle and the long side of the other baby triangle.Ĭompare the short side to the long side of each triangle and set them equal to each other. If we want to find Aybeesee's height, we can use the similarity of the triangles and make a proportion out of the sides.

The 'identical angles' kind of similar, not the 'Mary-Kate and Ashley Olsen' kind of similar. They might be different sizes, but these three right triangles are all similar. Knowing that, there's a possibility that Aybeesee is really two baby triangles in a cocktail dress. This line, called the altitude, splits her into two smaller right triangles. Well, her height is the length from point A, where her 90° angle is, down toward her hypotenuse at point D. She's a supermodel, so she's really proud of her height. Say that a triangle at the bar, named Aybeesee (or ABC for short), wants you to guess her height. Why would a right triangle ask you about geometric means? More importantly, how would a right triangle ask you about geometric means? Take the square root, and you're back to square one. If we cross-multiply, we can solve for the geometric mean and it'll give us the definition. Now, the reason this is helpful is because it lets the triangle know you care, and it comes from a proportion that looks like this: So if you're ever at a bar (drinking a Coca-Cola or chocolate milk, of course) and a right triangle asks you to find the geometric mean of 4 and 16, you won't break a sweat. Just multiply two numbers together and take the square root. To find altitudes of unruly triangles, we can just use the geometric mean, which actually isn't mean at all.

Altitude geometry example