A 45-45-90 triangle is a special type of right triangle that has two angles measuring 45 degrees and one angle measuring 90 degrees. This makes it both a right triangle and an isosceles triangle.
Here's a breakdown of its key characteristics:
- Angles: Its three angles measure 45 degrees, 45 degrees, and 90 degrees.
- Sides:
- The two sides opposite the 45-degree angles (the legs) are congruent (equal in length). This is what makes it an isosceles triangle.
- The side opposite the 90-degree angle (the hypotenuse) is longer than either leg.
- Relationship Between Sides: If the length of each leg is x, then the length of the hypotenuse is x√2. This relationship is crucial for solving problems involving 45-45-90 triangles.
Why is it Important?
The 45-45-90 triangle is important because knowing its angle-side relationships allows you to quickly determine the lengths of all sides if you know just one side length. This is extremely useful in geometry, trigonometry, and various applications in science and engineering.
Example:
If a 45-45-90 triangle has legs that are each 5 units long, then the hypotenuse is 5√2 units long.
In summary, a 45-45-90 triangle is a right isosceles triangle with specific angle and side relationships that make it easily solvable given minimal information.
