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: 

Isosceles Triangle  A triangle in which two sides are of the same length is called Isosceles Triangle
In this type of triangle: 

Equilateral Triangle  A triangle in which all three sides are of the same length is called Equilateral Triangle.
In this type of triangle: 
Some of the diagrams have been adopted from https://en.wikipedia.org/wiki/Triangle
Classification of Triangles based on the angles
Acuteangled Triangle  A triangle in which all the three angles are more than and less than is called acuteangled triangle.  
Rightangles Triangle  A triangle in which one of the angles is is called rightangled triangle.  
Obtuseangled triangle  A triangle in which one of the angles is more than but less than is called obtuseangled 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 midpoint of the opposite side of a triangle is called median.
In this vertex is meeting at point (such that ) midpoint of 

Centroid  The point of intersection of three medians is called centroid.  
Altitude  The perpendicular drawn from the vertex to the opposite side.
Here is the altitude of the triangle is the base. 

Orthocenter  The intersection of the three altitudes is called the Orthocenter of the triangle.
Here is the Orthocenter of the triangle. 

Angle Bisector  A line segment that bisects and interior angle of a triangle is called angle bisector.
Here is bisecting into two equal 

Incentre and Incircle  The point of intersection of internal angle bisectors is called the Incentre.
is the Incentre of the triangle. Now if you draw a circle with the center 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 

Circumcenter and Circumcircle  The point of intersection of the perpendicular bisectors of the sides of the triangle is called Circumcenter.
Here is the circumcenter. 

Exterior Angle and Interior Opposite Angles of a Triangle  is the exterior angle and and are opposite interior angles of this exterior angle. 
Some of the diagrams have been adopted from https://en.wikipedia.org/wiki/Triangle