Study Guide

Basic Geometry - Triangles

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Triangles are three-sided polygons, but we're sure that you already knew that. The triangle is the most sturdy of polygons. Its strong shape has been used to build buildings and bridges since the dawn of civilization. It has so much more muscle than a (wimpy) square. Think about it; that's why there are three legs on a tripod and three wheels on a tricycle.

Triangles can be classified (named) two ways: by their angles or by their sides. Here they are classified by angles:

  • Obtuse Triangle: has one obtuse angle (an angle greater that 90°).
  • Acute Triangle: has three acute angles (angles less than 90°).
  • Right Triangle: has one right angle (a 90° angle).

Obese, Acute, and Right Triangle

Here they are classified by sides (when the markings on the sides are the same, that means that the sides are congruent):

  • Equilateral Triangle: has three congruent sides.
  • Isosceles Triangle: has two equal sides.
  • Scalene Triangle: all sides are different lengths.

Equilateral, Isosceles, and Scalene Triangle

Here they are classified by both their angles and sides:

Triangles classified by angle and side

Regular Triangle

The interior angles of a triangle always add up to 180°, always. Since regular polygons have equal sides and angles, all equilateral triangles are regular. If we divide 180° into three angles, each angle of an equilateral triangle is 180 ÷ 3 = 60°.

Regular Triangle

Here's a video on interior and exterior angles, just to mix things up a little.

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