What is a scalene triangle? A triangle with three sides that have equal lengths is known as a scalene triangle. Since none of the three sides are equal, it follows that none of the three angles have the same degree. It is one of the three different kinds of triangles that may be differentiated from one another depending on the characteristics of their sides. As a result, we refer to the configuration of a triangle in which none of its sides are equal to a scalene triangle.
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What is a Scalene Triangle?
A scalene triangle is a kind of triangle with three sides that are each a distinct length, as well as three angles that each have a different measurement. Nevertheless, the total interior angles of the scalene triangle are unaffected by the multiple measures taken. The angle sum condition of a triangle is satisfied whenever a scalene triangle is considered because the sum of the three internal angles of a scalene triangle is always 180 degrees.
The fact that the three symbols on each side of the triangle shown above are distinct from one another demonstrates that the triangle’s sides are not equal to one another.
Properties of Scalene Triangle
A scalene triangle is a specific sort of triangle in which all three sides are of varying lengths and the total of the angles formed by the triangle’s three internal angles is equal to 180 degrees. It has a diverse set of characteristics. The scalene triangle has a number of significant features, some of which are listed below.
- The sum of the interior angles of a triangle is 180° (the sum of the interior angles of a triangle theorem).
- The length of each side is greater than the difference between the lengths of the other two sides and less than the sum of their lengths (triangle inequality).
- In a triangle, the side opposite the larger angle is the larger side. Conversely, the angle opposite the larger side is the larger angle (the relationship between the side and the opposite angle in a triangle).
- The three altitudes of a triangle intersect at a point called the orthocenter of the triangle (triangle concurrency).
- The three medians of a triangle intersect at a point. That point is called the centroid of the triangle. Also known as the three medians of the triangle converging at a point (converging at a point means passing through the same point). The distance from the centroid to the three vertices of the triangle is 2/3 the length of the median corresponding to that vertex. The median of the triangle divides the triangle into two parts of equal area (triangle concurrency).
- The three perpendicular bisectors of a triangle intersect at a point that is the center of the circumcircle of the triangle (triangle concurrency).
- The three internal bisectors of a triangle intersect at a point that is the center of the inscribed circle of the triangle (triangle concurrency).
- The theorem of cosine function: In a triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides minus twice the product of the lengths of those two sides and the cosine of the included angle.
- Sine function theorem: In a triangle, the ratio of the lengths of each side to the sine of the opposite angle is the same for all three sides.
- The median is the line segment connecting the midpoints of two sides of a triangle; a triangle with three medians. The midsegment of a triangle is parallel to the third side and is half its length. A new triangle formed by three medians in a triangle is similar to its parent triangle.
- In a triangle, the bisector of an angle divides the opposite side into 2 segments that are proportional to the 2 adjacent sides.
- In non-Euclidean geometry, a triangle can have the sum of three angles depending on the size of the triangle, as the size of the triangle increases, the sum approaches zero and has an infinite area.
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Difference Between Scalene, Isosceles, and Equilateral Triangles
On the basis of the lengths of their sides, triangles may be divided into three distinct categories: equilateral, isosceles, and scalene triangles. The following table provides an overview of the primary distinctions that can be made between the three distinct varieties of triangles.
| Equilateral Triangle | Isosceles Triangle | Scalene Triangle | ||
|---|---|---|---|---|
| A triangle is classified as equilateral if each of its three sides has the same length. | Isosceles triangles are those in which any two of the triangle's sides have the same length, regardless of which two sides they are. | A scalene triangle is one in which each of the triangle's three sides has a distinct measurement, as its name implies. | ||
| In a triangle with equilateral sides, each of the three angles has the same degree. Every angle is a full sixty degrees. | In a triangle with isosceles sides, the angles that are perpendicular to the sides that are equal are also equal (Isosceles Triangle Theorem) | The three angles that make up a scalene triangle each have a distinct measurement. |
Scalene Triangle Formula
There are two primary formulae that pertain to a scalene triangle. These formulas are concerned with the perimeter of a scalene triangle and the area of a scalene triangle, respectively.
The perimeter of a Scalene Triangle
The perimeter of a triangle is equal to the total of the three sides of the triangle, which is equal to the number of units that are denoted by the letters a, b, and c. As a result, the length of the perimeter of the scalene triangle is equal to (a + b + c) units, where a, b, and c refer to all three sides of the scalene triangle.
Area of a Scalene Triangle
The formula for calculating the area of a triangle is (1/2) b h square units. Here,
- The letter “b” indicates the base of the triangle.
- The letter “h” indicates how high above the triangle is.
Applying Heron’s formula is necessary in this case since we do not have the height or the base, but we do have the lengths of the sides of the triangle. As a result, the area of the scalene triangle is A = √s(s−a)(s−b)(s−c) square units. In this context, “s” refers to the semi-perimeter of a triangle, which may be calculated as follows: s = (a+b+c)/2, where “a,” “b,” and “c” stand for the three sides of the triangle.
Important Notes
- A scalene triangle is characterized by its three sides, which are all of varying lengths, and its three angles, which are all of varying degrees.
- Additionally, it adheres to the angle sum feature that the triangle has.
- A scalene triangle does not exhibit symmetry due to the lengths of the sides are not equal and even angles are of different measurements.
Triangles may be separated into three different types according to the lengths of the three sides of the triangle: equilateral triangles, isosceles triangles, and scalene triangles. The table that follows is an overview of the key differences that can be made between the three different kinds of triangles that are available.
In addition, the scalene triangle may be subdivided into the following three categories if the calculation is done according to the edge:
- Scalene triangles with a right angle have one angle that is 90 degrees and two other angles that have different degrees of angle measure. There is variation in the lengths of each of the three sides.
- In an acute scalene triangle, each of the three angles is less than ninety degrees, and the lengths of the triangle’s three sides are not equal.
- The obtuse scalene triangle is characterized by having one angle that is more than 90 degrees and two additional angles that are less than 90 degrees. One more time, the lengths of the three sides are not identical.
Recognizing a Scalene Triangle
Scalene triangles, like other triangles, consist of three sides and three angles that together add up to a total of 180 degrees. There is a lot of leeway in terms of the size and form of a scalene triangle, but there are a few criteria to keep in mind that will help you identify a scalene triangle as distinct from other types of triangles:
- You can determine the lengths of the three sides of any triangle provided that you have a ruler on hand. If the three sides are all of the varying lengths, then you have a scalene triangle.
- If you have access to a protractor, you should make use of it to determine the triangle’s angle measurements. Again, if none of them are the same as the others, then you have yourself a scalene triangle.
- If you do not have a method for determining the length of a triangle or the angles that it contains, it might be difficult to determine with absolute certainty whether or not the triangle is a scalene. Having said that, scalene triangles, by their very nature, are never symmetrical; as a result, they always have a bit of a “wonky” aspect to them, which may be a dead giveaway.
What is a scalene triangle? We believe you’ve got the answer. Hope that this article can be beneficial for you during the process of solving math problems. If you are planning to teach your kids about this essential topic, you can make your own collections of scalene triangle worksheets using our worksheet maker. Good luck!
