Which triangle can be used to explain the properties of 30-60-90 triangles?

In the context of explaining the properties of 30-60-90 triangles, the most relevant triangle is the equilateral triangle. An equilateral triangle has all three angles equal to 60 degrees and all three sides of equal length. When you consider an equilateral triangle and bisect it, you create two 30-60-90 triangles.

In a 30-60-90 triangle, the relationships between the lengths of the sides are well-known: the side opposite the 30-degree angle is half the length of the hypotenuse, and the side opposite the 60-degree angle is equal to the length of the side opposite the 30-degree angle multiplied by the square root of 3.

This specific triangle configuration is derived directly from the properties of the equilateral triangle, thus making it a crucial triangle for explaining the characteristics and relationships of 30-60-90 triangles. The other triangles mentioned do not have the same direct relationship to the 30-60-90 configurations. For example, a scalene triangle has no equal sides or angles, and an isosceles triangle has at least two equal sides but does not necessarily conform to the 30-60-90 relationships. A rhombus, while