Key Idea: Altitude in a Right Triangle

The altitude to the hypotenuse is a line drawn from the right angle of a right triangle perpendicular to the hypotenuse.
This altitude divides the original triangle into two smaller right triangles, and all three triangles are similar to each other.

General Rule:

• The altitude is perpendicular to the hypotenuse.

• It creates three similar right triangles:

  • The original triangle.

  • The triangle on the left of the altitude.

  • The triangle on the right of the altitude.

Why this matters for the SAT:

The similarity relationships allow you to set up proportions involving the altitude, the segments of the hypotenuse, and the legs. These relationships often lead to quick solutions for missing lengths without using trigonometry.