45-45-90 triangle

A 45-45-90 triangle is a special type of right triangle where the two angles are each 45 degrees, making the third angle 90 degrees. This triangle is isosceles, meaning its two legs (the sides opposite the 45-degree angles) are of equal length. The relationship between the lengths of the sides is consistent: if each leg is of length \( x \), the hypotenuse (the longest side opposite the right angle) will be \( x\sqrt{2} \). This property simplifies calculations in geometry and is frequently used in various fields, including architecture and design.