Classifying Triangles
There are two ways to classify triangles, as you can see in the examples above. You can measure their angles or their sides. The triangles that are classified by their angles include the following. Acute-angled triangles have three acute angles. Obtuse-angled triangles have ONE obtuse angle, as it is impossible to draw a triangle with more than one obtuse angle (try it). Right angled triangles have one right angle, as it is also impossible to have a triangle with two or more right angles. Triangles classified by their sides include the following. Scalene triangles have no equal sides and no equal angles. Isosceles triangles have two equal sides and two equal angles. Equilateral triangles have all sides and angles equal, and each angle is 60º (the angle sum of a triangle always equals 180º).
The angle sum of a triangle
As mentioned above, the angle sum of a triangle is always 180º. You can even prove it to yourself by following the instructions above in Working Mathematically.
Below is an example of how to find an unknown angle in a triangle. You will need to know this for the activities later on in the website.
Below is an example of how to find an unknown angle in a triangle. You will need to know this for the activities later on in the website.
To find the unknown angle in a triangle, just add up the two given angles and then subtract 180. It is a simple equation that takes seconds to solve. If you are given only one angle, but the triangle is an isosceles like shown above, then all you do is multiply the number by two (because two angles are equal) and subtract 180. This only works sometimes, as you might be given the angle that does't equal another one in that triangle.
Exterior angle of a triangle
To find the exterior angle of a triangle, first you have to extend one of the sides as shown above. Next, add up the two opposite interior angles, and that's the answer. It's as simple as that. You can even find an unknown interior angle by using this method. Extend the line where the unknown angle is, then find the exterior angle, and then subtract it by 180. This is shown in the above diagram.