Triangle:  We just studied polygons. Triangle is a polygon with three sides. So, we could define a triangle as a plane closed figure bounded by three line segments.

A triangle is a polygon with three edges and three vertices. It is one of the most basic shapes in geometry. A triangle with vertices A, B, and C is denoted by ∆ABC.

Kind of Triangles

Classification of triangles based on the length of the sides

 Scalene Triangle A triangle in which all three sides are of different lengths is called Scalene Triangle.   In this type of triangle: $\angle A \neq \angle B \neq \angle C$$\angle A \neq \angle B \neq \angle C$ Isosceles Triangle A triangle in which two sides are of the same length is called Isosceles Triangle In this type of triangle: $\angle B = \angle C$$\angle B = \angle C$ Equilateral Triangle A triangle in which all three sides are of the same length is called Equilateral Triangle.   In this type of triangle: $\angle A = \angle B = \angle C$$\angle A = \angle B = \angle C$

Some of the diagrams have been adopted from https://en.wikipedia.org/wiki/Triangle

Classification of Triangles based on the angles

 Acute-angled Triangle A triangle in which all the three angles are more than$0^{\circ}$$0^{\circ}$ and less than $90^{\circ}$$90^{\circ}$ is called acute-angled triangle. Right-angles Triangle A triangle in which one of the angles is $90^{\circ}$$90^{\circ}$is called right-angled triangle. Obtuse-angled triangle A triangle in which one of the angles is more than $90^{\circ}$$90^{\circ}$ but less than $180^{\circ}$$180^{\circ}$ is called obtuse-angled triangle.

Some of the diagrams have been adopted from https://en.wikipedia.org/wiki/Triangle

Term related to a Triangle

 Median A line segment joining the vertex to the mid-point of the opposite side of a triangle is called median. In this vertex $A$$A$ is meeting at point $D$$D$ (such that $BD=DC$$BD=DC$) midpoint of $BC$$BC$ Centroid The point of intersection of three medians is called centroid. Altitude The perpendicular drawn from the vertex to the opposite side. Here $AD$$AD$  is the altitude of the triangle $AD \ and\ BC$$AD \ and\ BC$ is the base. Orthocenter The intersection of the three altitudes is called the Orthocenter of the triangle. Here $A$$A$ is the Orthocenter of the triangle. Angle Bisector A line segment that bisects and interior angle of a triangle is called angle bisector. Here $AD$$AD$ is bisecting $\angle BAC$$\angle BAC$ into two equal $\angle BAD \ and\ \angle DAC$$\angle BAD \ and\ \angle DAC$ Incentre and Incircle The point of intersection of internal angle bisectors is called the Incentre. $I$$I$ is the Incentre of the triangle. Now if you draw a circle with the center $I$$I$  in such a way that it touches all the three sides of the triangle, then that is called Incircle. Perpendicular Bisector or Right Bisector A line bisecting any side of the triangle and perpendicular to it is called perpendicular bisector of that side of the triangle. Here BC is being bisected by $DE. BD=DC \ and\ ED\perp BC.$$DE. BD=DC \ and\ ED\perp BC.$ Circumcenter  and Circumcircle The point of intersection of the perpendicular bisectors of the sides of the triangle is called Circumcenter. Here $O$$O$  is the circumcenter. Exterior Angle and Interior Opposite Angles of a Triangle $\angle ACD$$\angle ACD$ is the exterior angle and$\angle CBA$$\angle CBA$  and$\angle BAC$$\angle BAC$  are opposite interior angles of this exterior angle.

Some of the diagrams have been adopted from https://en.wikipedia.org/wiki/Triangle