triangle introduction

Triangles

This table lists some essential facts about triangles that will be used throughout the discussion of the trigonometric ratios. Although right triangles will be of special concern early on, triangles in general will be covered so all of the basic terms are presented here.

A triangle is any three-sided polygon. The corners are called vertices of the triangle.
The sum of the angles in any triangle is 180o.
The longest (shortest) side is opposite the largest (smallest) angle.
A right triangle is one that contains a right angle. The other two angles must then be complementary acute angles.
An isosceles triangle is one having two sides of equal length. The angles opposite these two sides are of equal measure.
An equilateral triangle is one having all three sides of equal length. The three angles are all of measure 60o.

One of the distinguishing properties of right triangles is the Pythagorean Theorem. The importance of this property lies in the fact that the length of a side of a right triangle can be computed if the other two side lengths are known.

Pythagorean Theorem

Given a right triangle, the lengths of its sides satisfy the square relation shown on the left.