Classify Triangles in Geometry
A common task in basic geometry is to classify triangles according to the definitions of various terms. Some triangles can be classified by only term, and some triangles fall into two overlapping, non-mutually-exclusive categories. This article shows you the simple steps for performing this task.
Instructions
1. First see if the triangle has three equal sides, and therefore three equal angles. If it does, then the triangle is called equilateral. The sum of the angles in any triangle is 180°, so notice how each angle here is 60°. Of course all the sides are congruent (equal in length) as well.
2. Next, see if the triangle has two equal sides, and one unequal. If so, it is referred to as isosceles. The tick marks in the picture show the two sides that are equal, and the angle marks show that the two opposite angles are equal. We often need to use this information to solve a geometry problem which has missing values. Note that an isosceles triangle could be further classified as acute, right, or obtuse, discussed in a later step.
3. Next, see if the triangle contains a right (90°) angle, as shown. If it does, then it is called a right triangle. The other two angles will add up to 90°, since we've already used 90 out of the 180 total degrees for the right angle. Note that if sides a and b in this diagram were equal, then we would say that the triangle is right isosceles. Make sure you see that the definition of isosceles would also be met. The triangle would have two equal sides, and one unequal (the hypotenuse c). The angles opposite sides a and b would be equal.
4. If a triangle has sides of three different lengths, and therefore three different angles, we call it a scalene triangle. If we were only given one of the three angle measurements, we would have no way of determining the other two, unless we had some additional information.
5. Just like with isosceles triangles, we can also add an additional classification to scalene triangles. If the triangle contains a right angle, we would add the term "right," as in "right scalene." If the triangle contains an obtuse angle (an angle between 90° and 180°) we would add the term "obtuse," as in "obtuse isosceles." If the triangle contains three acute (less than 90°) angles, we would add the term "acute" to describe it, in addition to "isosceles" or "scalene."
6. Note that an equilateral triangle is automatically acute by definition, since it has three 60° angles. Also note that a right triangle can never be obtuse. It already has a 90° angle, and each of the other two angles have to be smaller than 90°, as well as add up to 90°.
7. Students should be certain to memorize these terms, and make sure that they understand solve geometry problems involving these types of triangles, with an emphasis on problems that contain missing angle measurements that can be deduced from these definitions.
Tags: triangle contains, equal sides, Note that, right angle, would term, angle measurements, Classify Triangles