What are the types of triangles
A triangle is a polygon with three sides. It is one of the basic shapes in plane geometry. Before we find out the types of triangles, let's look at how to construct a triangle.
The elements of a triangle
One of ways to construct a triangle is by 3 separate points. A triangle can be made by simply joining the 3 points. In the meantime, the basic elements of the triangle are also constructed.
Vertices: the original 3 points which construct the triangle are the vertices of the triangle. They are endpoints of 3 sides. If a triangle is made by 3 given lines, the intersection points of separate two lines construct vertices of the triangle.
Sides: line segments that join two consecutive vertices and form a closed two-dimensional shape. In a triangle, the sum of the length of two sides is larger than the third side.
Interior angles: angles that are formed by two consecutive sides at the vertex where they converge. The sum of three interior angles of a triangle is 180°.
There two ways to classify triangles. Triangles can be classified either according to their sides or according to their interior angles. So we will elaborate from the two different criteria.
Types of triangles by sides
With the difference of its sides, a triangle can be equilateral, scalene or isosceles triangle.
1. Scalene Triangle
A scalene triangle is a triangle that has all its three sides in different length, which means all of its interior angles are also of different measures.
2. Isosceles Triangle
An isosceles triangle is a triangle that has two of its sides in equal length. In other words, an isosceles triangle has one vertex angle and two congruent base angles.There are some special cases for isosceles triangles, such as equilateral triangle, isosceles right triangle, golden triangle if their sides meet certain criteria.
3. Equilateral Triangle:
As mentioned above, equilateral triangle is a special case of isosceles triangle. If all of its three sides have the same measurements, the triangle is called an equilateral triangle. For an equilateral triangle, all of its interior angles are also equal. An equilateral triangle is also called median triangle.
Types of triangles by angles
According to the difference of angles, a triangle can be acute, obtuse or right triangle.
1. Acute Triangle
A triangle which has all its three interior angles less than 90° or acute , is called an acute angled triangle or acute triangle. An acute triangle can be equilateral, scalene or isosceles triangle.
2. Obtuse Triangle:
If one of the three angles of a triangle is an obtuse angle, i.e., larger than 90° and less than 180°, the triangle is an obtuse angled triangle or obtuse triangle. One triangle has only one angle that can be obtuse, or the sum of the three angles will be larger than 180°, which is impossible.
3. Right Triangle:
A right triangle or right-angled triangle is a triangle with one of its angle right angle. In other words, one of the angles of the triangle is 90°, the sum of the other two is also 90°.
Steven Zheng
posted 3 years ago