The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

You might have come across an enclosed shape with three pointed tips; it is known as a **triangle**. A **triangle** is a polygon shape with three vertices and three edges. Being an enclosed shape with three sides, a **triangle** also has three angles whose sum is always 180 degrees. **Triangle** is one of the basic shapes in geometry. There are two ways to categorize **triangle**s: the length of their sides or by their angle. Classifying **triangles** based on length are derived: isosceles **triangle**, equilateral **triangle**, and scalene **triangle**.

A scalene **triangle** is the type of **triangle** whose all three sides tend to have different lengths and different angles. Some of the right-angled **triangle**s are scalene if the other two angles and sides are not congruent. Due to this reason, no line of the scalene **triangle** is in symmetry. Additionally, the angle opposite the longest side is generally the largest angle, while the small side’s angle is the smallest. Lack of symmetry is the key feature of this sort of **triangle**. The formula for calculating a scalene **triangle** area is half times the product of its height and base length. For more information on this sort of **triangle**, go through the resource library on MSVgo.

The **triangle** with two equal sides and two equal angles is known as an isosceles **triangle**. The name ‘isosceles’ is derived from two Greek words: Iso, meaning same, and Skelos means legs. In an isosceles **triangle,** there are two same base angles with one other angle. The area of an isosceles **triangle** is calculated with the formula (b/4) * √(4a2 – b2), and its altitude is calculated with the formula (b/2a) * √(4a2 – b2). Key examples of isosceles **triangles** seen in the modern world are the faces of bipyramids and most of the Catalan solids. Since ancient times, the isosceles **triangle** was used in architecture and design to structure the pediments and gables of the constructed buildings. For more information on this sort of **triangle**, go through the resource library on MSVgo.

The equilateral **triangle’s basic nature** is that it has three equal sides and three congruent angles of F degrees. If a perpendicular is drawn from its vertex, the opposite sides are bisected into equal halves. The ortho-center and centroid of the equilateral **triangle** are always at the same point. The area of an equilateral **triangle** is derived with formula √3a2/4, where a is the side. Additionally, the median, angle bisector, and altitude of the sides of the equilateral **triangle** are always the same. For more information on this sort of **triangle**, go through the resource library on MSVgo.

A **triangle** whose all three angles are less than 90 degrees is known as an acute angle **triangle**. The formula for calculating an acute angle **triangle** area is half the product of base and height, while its perimeter is the addition of the length of all three sides. Equilateral **triangle**s are always acute angle **triangles** as all its angles are 60 degrees. Additionally, if a line is drawn from the acute angle **triangle** base to the opposite vertex, it is always perpendicular to the base. For more information on this sort of **triangle**, go through the resource library on MSVgo.

The right-angle **triangle** is the **triangle** whose one angle is 90 degrees. This sort of **triangle** is the most used shape in mathematics due to its implications in Pythagoras theorem and trigonometry. Concerning the Pythagoras theorem, the right angle triangle depicts that hypotenuse is always the root of the sum of the squares of the base side and perpendicular side. On the other hand, the right-angle **triangle** is used in trigonometry as it always reflects the presence of three angles in the first quadrant due to the 90 degrees angle; thus, the values of sine, cos, and tan are derived easily using it. The first quadrant also reflects positive values, and the only sin, cos, and tan are positive in the first quadrant, while they change the value in the other three quadrants. Right angle **triangle** can be scalene or isosceles but never equilateral **triangle** as one of its angles is 90 degrees. For more information on this sort of **triangle**, go through the resource library on MSVgo.

An obtuse angle **triangle** is a **triangle** with one obtuse angle and two acute angles. There can be only one obtuse in a **triangle** because the sum of all the angles for a **triangle** is 180, and as per the definition of the obtuse angle, it is higher than 90 degrees. Thus, having two angles greater than 90 degrees will take the sum of the three angles to more than 180 degrees. For more information on this sort of **triangle**, go through the resource library on MSVgo.

Overall, the **triangle** is an enclosed geometrical shape with three sides, three angles, and three vertices. There are key basic types of **triangle**s: the scalene **triangle**, isosceles **triangle**, and the equilateral **triangle**. There are three other sorts of **triangles:** acute angle **triangle, right**-angle **triangle**, and obtuse angle **triangle**.

**What are the six types of triangles?**

The six types of **triangle**s are scalene **triangle**, isosceles **triangle**, equilateral **triangle**, acute angle, **triangle, right**-angle **triangle**, and obtuse angle **triangle**.

**What are the three main types of triangles?**

The three main types of **triangles** are scalene **triangle**, isosceles **triangle**, and equilateral **triangle**.

**What are the five properties of a triangle?**

The five properties of a **triangle** are:

- It has three sides
- It has three vertices
- It has three angles
- The sum of the internal angles of a
**triangle**is always 180°. - The area of a
**triangle**equals half the product of its height and base

**What are congruent triangles in geometry?**

If two angles and the included side of one **triangle** are similar to the corresponding constraints of another **triangle**, then both the **triangle**s are said to be congruent.

For more fun and interactive lessons on Triangles, visit the MSVgo application.