Triangle and Its Various Kinds of Centres

A triangle is a three-sided polygon with three edges and three vertices in geometry. The most significant feature of a triangle is that the sum of a triangle’s interior angles equals 180 degrees. This is the angle sum property. We’ve included key triangular notes to help you get the most out of the Mathematics part. Let’s look at the properties of triangles and different kinds of centres that you should know. 

We can define a triangle as a polygon with 3 angles and sides with the sum of all three angles equaling 180°.

Properties of a Triangle

Here are the various characteristics of a triangle:

• There are three sides, three angles, and three vertices in a triangle.
• The total of a triangle’s internal angles is always 180 degrees. This is the angle sum property of a triangle.
• The length of any two triangle sides added together is greater than the length of the third side.
• The greatest side of a triangle is the side opposite the largest angle.
• The sum of the triangle’s internal opposite angles is equal to any of its outer angles. This is referred to as a triangle’s outside angle property.

Different Kinds of Centres You Should Know

The Centroid

The centroid of a triangle is found by connecting the midpoints of each leg of the triangle to the opposing vertex of any triangle. The median is the line segment formed by connecting these spots.

The Circumcenter

The circumcenter is the point on the circle when all three vertices are the same distance apart. The distance between the circumcenter and any of the triangle’s three vertices is thus the radius of the circle. It is discovered by locating the midpoints of each triangle leg and drawing a line perpendicular to that leg at its midpoint.

The Orthocenter

The position of the orthocentre inside the triangle is the point where the elevations of each side meet to form a triangle. A triangle’s altitude is determined by dropping a line perpendicular to the opposing side from each vertex. The height of a triangle is also referred to as its altitude. Remember that unless you have a particular triangle, such as an equilateral triangle, the altitudes of a triangle do not pass via the midpoints of the legs.

The Incenter

The incenter is the final triangle centre we’ll look into. It’s the point on the inside of the triangle that forms the origin of a circle. The incenter, like the centroid, is always inside the triangle. The intersection of the angle bisectors of the triangle’s three vertices is used to create it. Dropping a perpendicular from the incenter to any of the triangle legs yields the radius of the circle.

Key Takeaways

• The lengths of any two triangle sides added together are always bigger than the length of the third side
• Similarly, the length difference between any two triangle sides is always less than the length of the third side
• The shortest side is the side opposite the smallest interior angle and vice versa. Similarly, the longest side is the side opposite the biggest interior angle and vice versa
• A triangle’s height is equal to the length of the perpendicular that runs from a vertex to the opposite side, which is called the base

Conclusion

That’s a wrap to the introduction to Triangle and its various kinds of Centres!

A triangle has three straight sides and is a polygon. A triangle centre is a point for which a triangle centre function can be defined and is given in terms of the triangle’s side lengths and angles. Check all of the triangle centre boxes once you’ve identified the distinct triangle centres. Adjust the triangles’ vertices and take note of the qualities of each of the centres.