Triangle:
A triangle is a closed curve which is formed by 3 line segments. The line segments by which the triangle is formed are called sides of the triangle. The points of intersections of the sides of the triangle are called the vertices of the triangle. The angles formed at the vertices are called the angles of the triangle.
Triangle is a basic shape which has several properties based on its sides, interior angles and exterior angles.
a) Medians of a triangle:
A line drawn from any vertex to the mid point of its opposite side is called a median with respect to that vertex. Thus, a triangle has 3 medians and all the 3 medians meet at one point. i.e. the medians of a triangle are concurrent.
The point of concurrency of medians is called centroid of the triangle.
b) Altitudes of a triangle:
A perpendicular line segment drawn from a vertex to its opposite side is called the altitude of the triangle with respect to that vertex. Thus, a triangle has 3 altitudes and all the 3 altitudes meet at one point. . i.e. the altitudes of a triangle are concurrent.
The point of concurrency of altitudes is called orthocenter of the triangle.
c) Angular bisectors:
The bisectors of the angles in atriangle meet at one point. i.e. the angular bisectors of a triangle are concurrent.
The point of concurrency of altitudes is called incenter of the triangle.
d) Exterior angle property:
An exterior angle in a triangle is equal to sum of two opposite interior angles.
Here, ∠4 = ∠1 + ∠2.
e) Angle sum property:
The sum of all interior angles in a triangle is 1800.
The sum of all exterior angles in a triangle is 3600.
This property is mostly used in finding an angle in a triangle when we know only two angles.
f) Sum of the sides of the triangle property:
The sum of any two sides of a triangle is always greater than the other side.
Here,
a+b>c;
b+c>a;
c+a>b.
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