Geometry · Similarity & Right Triangles

45-45-90 Triangle

HSG-SRT.C.8

Definition

An isosceles right triangle whose hypotenuse equals a leg times the square root of 2.

Examples

  • If each leg is 1, the hypotenuse is the square root of 2, giving a side ratio of 1 : 1 : root 2.
  • If each leg is 5, the hypotenuse is 5 times the square root of 2.

Key rule

In a 45-45-90 triangle, the two legs are always equal.

Memory hook

Equal legs, hypotenuse is a leg times the square root of 2.