Classifying two-dimensional shapes

Different categories of triangles - part 1

There are basically two ways of categorizing triangles. The first is based on their angles, the second on their sides.

First, we can categorise a triangle as being acute angled, right angled or obtuse angled. An acute-angled triangle is one in which all three angles are acute, that is, less than 90 degrees. A right-angled triangle is one in which one of the angles is a right angle; it is not possible, of course, to have two right angles since the sum of the three angles has to be 180 degrees, and this would make the third angle zero! An obtuse-angles triangle is one with an obtuse angle, that is, one angle greater than 90 degrees and less than 180 degrees; again it is possible to have only one such angle because of the sum of the three angles having to equal 180 degrees. This condition also makes it impossible to have a triangle containing a reflex angle.