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