The Triangle and its Properties
A triangle is a simple closed curve formed by three line segments. The six elements of a triangle are its three angles and the three sides. Based on the sides of a triangle, it can be classified as scalene, isosceles and equilateral triangle. Based on the angles of a triangle, it can be classified as acute-angled, obtuse-angled and right-angled triangle.
A line segment drawn from one vertex to the midpoint of the opposite side of the triangle is called the median of the triangle. A triangle has 3 medians. The medians of a triangle are concurrent and the point of concurrency is known as the centroid of the triangle.
The altitude of a triangle is a perpendicular from one vertex of the triangle to the opposite side. A triangle has 3 altitudes. The altitudes of a triangle are concurrent and the point of concurrency is known as the orthocentre of the triangle.
An exterior angle of a triangle is equal to the sum of its two interior opposite angles.
Angle Sum property of a triangle states that sum of all interior angles of a triangle is equal to 180°.
Equilateral triangle is a triangle in which all the three sides are equal in length and the measure of each angle is 60°.
Isosceles triangle is a triangle in which two sides are equal in length and the angles opposite to the equal sides are also equal.
The sum of the lengths of any two sides of a triangle is greater than the third side. The difference between the lengths of any two sides of a triangle is smaller than the length of the third side.
In a right-angled triangle the side opposite to the right angle is called the hypotenuse. Base and altitude are called the two legs of the right-angled triangle.
Pythagoras Theorem states that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of other two sides.
Converse of Pythagoras Theorem states that in a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite to the first side is a right angle.
Keywords: Incentre, Circumcentre