Chapter 4

Triangle Fundamentals


Bullet Classifying triangles by their angles

Bullet Uncovering the triangle inequality principle

Bullet Poring over the Pythagorean Theorem

Considering that it’s the runt of the polygon family, the triangle sure does play a big role in geometry. Triangles are one of the most important components of geometry proofs. They also have a great number of interesting properties that you might not expect from the simplest possible polygon. Maybe Leonardo da Vinci (1452–1519) was on to something when he said, “Simplicity is the ultimate sophistication.”

Taking in a Triangle’s Sides

Triangles are classified according to the length of their sides or the measure of their angles. These classifications come in threes, just like the sides and angles themselves.

The following are triangle classifications based on sides:

  • Scalene: A triangle with no congruent sides
  • Isosceles: A triangle with at least two congruent sides
  • Equilateral: A triangle with three congruent sides

Scalene triangles

In addition to having three unequal sides, scalene triangles have three unequal angles. The shortest side is across from the smallest angle, the medium side is across from the medium ...

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