The Golden Triangle is a specific isosceles triangle with unique angle and side properties tied to the golden ratio.
Defining the Golden Triangle
The Golden Triangle is defined as:
- An isosceles triangle.
- Vertex angle: 36 degrees.
- Base angles: 72 degrees.
- Side Lengths: The ratio of the length of a leg to the length of the base is the golden ratio (approximately 1.618).
Properties and Characteristics
The Golden Triangle's special properties arise from its relationship with the golden ratio.
- Golden Ratio: The legs are in golden ratio (proportion) to the base.
- Angle Bisection: When a base angle is bisected, the angle bisector divides the opposite side (a leg of the original triangle) in a golden ratio.
- Smaller Isosceles Triangles: This bisection creates two smaller isosceles triangles. One is similar to the original Golden Triangle, and the other is also an isosceles triangle.
Visual Representation
It helps to visualize the Golden Triangle:
| Feature | Description |
|---|---|
| Type | Isosceles Triangle |
| Vertex Angle | 36° |
| Base Angles | 72° |
| Side Ratio | Leg : Base = Golden Ratio (φ) |
