In a 45-45-90 right triangle, both of the non-hypotenuse angles are 45 degrees. This type of triangle is also known as an isosceles right triangle, where the two legs opposite the 45 degree angles are of equal length.
Here’s the reasoning:
1. Equal Angles: Since the triangle has two 45 degree angles, the sides opposite those angles must be equal in length. This is due to the properties of isosceles triangles, where two sides are of equal length because the two base angles are equal.
2. Legs' Lengths: Let's denote the length of each leg as [tex]\( l \)[/tex]. Because both legs are equal, the ratio of one leg to the other is [tex]\( \frac{l}{l} \)[/tex].
3. Simplified Ratio: Simplifying the ratio [tex]\( \frac{l}{l} \)[/tex], we get 1.
Therefore, the ratio of the length of one leg to the length of the other leg in a 45-45-90 right triangle is [tex]\( 1:1 \)[/tex].
Thus, the correct answer is:
[tex]\[ \boxed{1:1} \][/tex]
This corresponds to option D.
