Types of Triangles Explained

Triangles are the simplest polygon — three sides, three angles — but they come in many varieties. Here's a complete guide to every triangle type.

By Side Length

• Equilateral: All 3 sides equal, all 3 angles = 60°. The "perfect" triangle that our drawing challenge tests!
• Isosceles: 2 sides equal, 2 angles equal. Common in architecture (roof gables)
• Scalene: No sides equal, no angles equal. The most "random" triangle type

By Angle

• Acute: All angles less than 90°. Every equilateral triangle is also acute
• Right: One angle is exactly 90°. The basis of trigonometry and the Pythagorean theorem (a² + b² = c²)
• Obtuse: One angle greater than 90°. Appears "squished" or "leaning"

Special Triangles

• 30-60-90 triangle: Side ratios are 1 : √3 : 2. Half of an equilateral triangle
• 45-45-90 triangle: Side ratios are 1 : 1 : √2. Half of a square cut diagonally
• 3-4-5 triangle: The simplest right triangle with integer sides. Builders use this to check right angles
• Golden gnomon: A triangle with angles 36°-36°-108°, related to the golden ratio

Why Triangles Are the Strongest Shape

Triangles are the only polygon that is inherently rigid. A square can be pushed into a parallelogram, but a triangle cannot be deformed without changing the length of a side. This is why:

• Bridges use triangular trusses
• Roof structures are triangular
• 3D models are built from triangles (every surface in a video game is made of triangles)
• The Eiffel Tower is constructed from thousands of triangles

Essential Triangle Formulas

• Area: A = ½ × base × height
• Perimeter: P = a + b + c
• Pythagorean theorem: a² + b² = c² (right triangles only)
• Sum of angles: Always = 180°
• Heron's formula: A = √(s(s-a)(s-b)(s-c)) where s = (a+b+c)/2

Draw a Perfect Triangle

Can you draw a perfect equilateral triangle freehand? Take the challenge and get scored on side equality, angle accuracy, and straightness!