Did you know that naming and identifying shapes is a skill that takes a long time to develop? Adults may wonder why that is so, considering that they are easily recognizable and differentiable. Unlike adults, children don’t find this simple activity as easy.
They have to learn and understand the different properties of each shape, their number of dimensions, etc. Children don’t find all of this as easy as walking a dog, which is why it is advised to spend lots of time going over them at an early age so that their knowledge concerning the shapes is solidified.
However, as people grow old, some of them tend to forget many things about shapes. Although they know what each shape looks like, they are hardly able to tell anything else about them beyond that. This is why our discussion today is based on one of the most easily identifiable shape that every reader must be familiar with – Triangle.
So in this post, we’ll talk about different types of triangles to help brush up your geometry knowledge. But before we delve into it, let’s go over when the first triangle was made.
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A triangle is often referred to as “Pascal’s triangle” as Blaise Pascal is touted as the inventor of Triangle in the 16th century.
However, history shows that several other mathematicians knew about it even before Pascal was born. The triangle was discovered by a Persian mathematician – Omar Khayyam – and a Chinese mathematician – Chia Hsien – separately thousands of years ago. The triangle is also mentioned in a 10th century manuscript of Saint Emmeram that is well preserved in the library of Monaco.
The French mathematician – Pascal is credited for originating various types, properties, and various applications of triangles. Out of these, we’ll now discuss, as mentioned above, the fundamental types of triangles.
In geometry, there are five fundamental types of triangles – equilateral triangle, isosceles triangle, scalene triangle, right triangle, and oblique triangles. Each of them has a distinct shape, properties, and formulas which are explained in detail below.
An equilateral triangle consists of three equal sides which means they have identical sides as well as angles. Regardless of the length of their sides, all the angles in equilateral triangles have a total angle of 60 degrees.
Since the angles of each side are equal, the internal angles of any triangle add up to 180 degrees and therefore, each angle is 60 degrees. As the equilateral triangle has three equal angles, the total degrees can easily be divided by 3. Hence, each angle of an equilateral triangle is 60 degrees, making it an acute triangle.
In an equilateral triangle, every altitude is also a median and a bisector, every median an altitude and a bisector, and every bisector an altitude and a median. Those who don’t know what median, altitude, and bisector mean, here’s a concise explanation:
An altitude of a triangle is a line that passes through a vertex and meets the opposite side making a right angle. A median in a triangle is a line segment that starts from a vertex (a corner point of a triangle) to the center point of the opposite side. On the other hand, a bisector is a line perpendicular to another side and goes through the midpoint.
An isosceles triangle has two equal sides and this is why two of its angles are equal as well. The base of the isosceles triangle is shorter in length and the other two sides are similar in length. By measuring either of the two angles, the third angle can be measured. It must be noted that isosceles triangles are acute triangles as the largest angle it can have is less than 90 degrees.
In an isosceles triangle, the altitude to the base is the perpendicular bisector of the base; it is also the angle bisector of the vertex angle, line of symmetry of the triangle, and the median from the apex to the base as well. This means that the circumcenter, incenter, centroid, and orthocenter all fall on the altitude to the base. This property makes the altitude to the base an Euler line of the triangle as it passes through several significant triangle centers (incenter, centroid, circumcenter, and orthocenter).
A scalene triangle has a completely different side length with different measurments. In other words, none of the sides of the scalene triangle are identical.
Generally, other types of triangles add up to 180 degrees but the interior angles of a scalene triangle are different. For instance, a triangle with 40 degrees, 50 degrees, and 90 degrees angles is a scalene triangle as each angle is different from one another.
However, a triangle with 40 degrees, 40 degrees, and 90 degrees cannot be considered as a scalene triangle since two out of the three angles are same. Due to this main property, scalene triangles are different from the above two types of triangles.
Also known as the right-angled triangle, this type of triangle has one of its interior angles at 90 degrees. It is a common type of triangle that appears prominently in various branches of math such as trigonometry as it includes the study of the properties of right triangles and the Pythagoras theorem which deals with the relationship between all the three sides of a right triangle.
One of the constant attributes of a right triangle is that the opposite side of the right angle is always the longest side; this longest side is called “hypotenuse”. The other two sides, that aren’t hypotenuse, make up the right angle.
A right triangle can also be an isosceles if two of the three angles are identical in length. However, a right triangle can never be equilateral since the opposite side of the right angle is longer than the other two sides.
5. Oblique Triangle
Oblique triangles are further divided into two types:
As an acute angle is an angle that is less than 90 degrees; similarly, an acute triangle is a triangle that has three angles that are smaller than 90 degrees. The question that arises is how can one tell if a triangle is an acute triangle? Measure all the three angles and if they are less than the right angle i.e., 90 degrees, then it is an acute triangle.
There are other types of triangles that can also come under the acute triangle. You can find that out by reading the definition of the acute triangle. However, there are other ways to find out whether a triangle is an acute triangle or not.
As we all know that the sum of a triangle is 180 degree. Therefore, two angles of an acute triangle have to be identical while the third angle is different. For instance, if the two angles of an acute angle are 50 degrees each and the third degree is an 80. This way, the total angle of the triangle is 180 degrees.
An obtuse triangle is the type of triangle that has an angle greater than 90 degrees. This means that the other two angles have to be less than 90 degrees so that they add up to 180 degrees in total.
The longest side of an obtuse triangle is always opposite the obtuse angle vertex. An obtuse triangle can either be an isosceles or scalene. To find an area of a triangle, ½ the length of the base is multiplied by its height. In order to find out the height of an obtuse triangle, you will need to draw a line from the outside of a triangle all the way to its base.
Trivia: A special obtuse isosceles triangle is the calabi triangle, the only non-equilateral triangle, in which the biggest square that is situated in its interior can be positioned in three different ways.
So which of these types of triangles did you not know much about?