Triangles Classification

Triangles are classified, or grouped, in two different ways. One classification distinguishes among the sides,

and another by the angles. For a triangle, you can have all three sides congruent (equal measure), or two sides congruent, or no sides congruent. Congruent sides and congruent angles of triangles are often marked as in the following figure.

The following diagram shows the classification names when grouping by sides.

Note that isosceles triangles have two sides congruent, called the legs, and also two angles congruent, called the base angles. The non-congruent side is called the base. Equilateral triangles have all sides and all angles congruent. Each of the angles in an equilateral triangle has measure of 60°.
The classification of triangles according to angle measure is shown in the following figure.

Be careful when classifying triangles by angle measure; notice that even though right triangles and obtuse triangles each have two acute angles, their classification is not affected by these angles. Acute triangles have all three acute angles.

Example:
Classify this triangle by sides and angles.

To group by sides, notice that there are two sides (AB, BC) that are congruent. The side classification is isosceles. To group by angles, note that there is a right angle in this triangle. So, the classification is right isosceles.

Example:
Classify this triangle by sides and angles.

Because no sides are marked as congruent in this figure, the classification by sides is scalene. There is one angle greater than 90° ( angle B is 110°); therefore, the angle classification is obtuse. This triangle is obtuse scalene.

Math test: classifying triangles