In this video, we are going to learn about the proportions that exist when a perpendicular line is drawn from the right angle of a right triangle to the hypotenuse. The result is the formation of two smaller, similar right triangles.

Here, we have a large right triangle. After drawing a perpendicular line straight down to the hypotenuse from the right angle, it forms two smaller right triangles. These 3 right triangles are all similar, meaning that corresponding parts are in proportion to each other.

As shown in the video, we will label the different sides as a (leg 1), (leg 2), c (hypotenuse), h (altitude), x (projection 1), and y (projection 2). Based on this diagram there are a few proportions that should be remembered:
$\dfrac{x}{a}=\frac{a}{c}$
$\dfrac{y}{b}=\frac{b}{c}$
$\dfrac{x}{h}=\frac{h}{y}$

*Note that if we are missing sides when trying to solve for these proportions, we can always use the Pythagorean Theorem to find the missing sides.
*Remember the following statement: The product of the means is equal to the product of the extremes. This applies to all three proportions listed above.