Final answer:
Triangles can be named based on sides: equilateral, isosceles, and scalene; or based on angles: right, acute, and obtuse. This classification helps in understanding their properties and applying trigonometry.
Step-by-step explanation:
Triangles are classified based on two main characteristics: by their sides and by their angles. When naming triangles by their sides, we look at the lengths of the sides. A triangle with all sides of equal length is called an equilateral triangle. If only two sides are of equal length, it's called an isosceles triangle, and if all sides are of different lengths, it's called a scalene triangle.
When classifying triangles by their angles, we refer to the measures of the angles. A triangle with one right angle is known as a right triangle. If all angles are less than 90 degrees, it's an acute triangle, and if one angle is greater than 90 degrees, it's an obtuse triangle.
Understanding these distinctions helps in studying their properties and the application of trigonometry, which is the relationship between the angles and sides of right-angled triangles. Trigonometric ratios such as sine, cosine, and tangent are based on the relationships between the sides of a right triangle.