ACCESS TO GEOMETRY THROUGH ORIGAMI
Understanding Triangles in Origami
This page explains more about triangles in very basic terms. The info is meant to be helpful and should, hopefully, come in handy when doing origami. You can also find links to text tutorials on how to create different triangles using origami techniques.
Classification by Side Lengths
Triangles may be classified in different ways depending on their side lengths:
Equilateral Triangle
- Sides: All three sides are exactly equal in length.
- Angles: All three inner angles are equal, measuring sixty degrees each.
Isosceles Triangle
- Sides: Two sides are equal in length, and one side is different (the base).
- Angles: The two angles opposite the equal sides are also equal to each other.
Scalene Triangle
- Sides: All three sides have different lengths.
- Angles: All three inner angles have different measurements.
Classification by Angles
You may also come across triangles classified by their angles, as follows:
Right-Angled Triangle
Definition: Has one angle that measures exactly ninety degrees (a square corner). The side opposite this right angle is the longest side, called the base or hypotenuse.
Acute Triangle
Definition: All three inner angles are sharp—meaning each one is less than ninety degrees. An equilateral triangle is a classic example of an acute triangle.
Obtuse Triangle
Definition: Has one wide angle that measures greater than ninety degrees. The remaining two angles are both sharp (less than ninety degrees).
Basic Facts
The following are just some basic facts to keep in mind when working with triangles:
1. What Makes a Triangle a Triangle?
- Three Sides, Three Corners: A triangle is any flat shape formed by connecting three straight lines. The corners where two lines meet are called vertices (or a vertex if you are talking about just one corner).
- Always Closed: All three sides must connect completely with no gaps or open ends.
- Straight Lines Only: If any side is curved, it is not a triangle.
2. The Golden Rule: The 180-Degree Sum
- The Magic Number: If you add up the measurements of all three inner angles of any triangle, they will always total one hundred and eighty degrees.
- It Never Changes: Whether the triangle is tiny, huge, tall, flat, symmetrical, or completely lopsided, the three angles always add up to one hundred and eighty degrees.
3. Why Triangles Are So Strong (Rigidity)
- The Strongest Shape: Unlike squares or rectangles, which can easily wobble, collapse, or bend into rhombuses when you push on their corners, a triangle cannot change its shape without breaking or bending one of its sides.
- Where We See It: This is why engineers use triangles everywhere in the real world—in bridges, roof trusses, construction cranes, and radio towers.
Folding Triangles with Origami
Though squares are most often used in origami, rectangles and triangles can also be used, especially for modular origami. The links below will help you to create triangles from squares and/or rectangles: