The Triangle and its Properties
A triangle having all three unequal sides is called a Scalene Triangle.
A triangle having two equal sides is called an Isosceles Triangle.
A triangle having three equal sides is called an Equilateral Triangle.
If each angle is less than 90°, then the triangle is called an acute angled triangle.
If any one angle is a right angle then the triangle is called a right angled triangle.
If any one angle is greater than 90°, then the triangle is called an obtuse angled triangle.
An exterior angle of a triangle is equal to the sum of its interior opposite angles.
The total measure of the three angles of a triangle is 180°.
The sum of the lengths of any two sides of a triangle is greater than the third side.
In a right angled triangle, the sides have some special names. The side opposite to the right angle is called the hypotenuse; the other two sides are known as the legs of the right-angled triangle.
In a right-angled triangle, the square on the hypotenuse = sum of the squares on the legs.
1. The six elements of a triangle are its three angles and the three sides.
2. The line segment joining a vertex of a triangle to the mid point of its opposite side is called a median of the triangle. A triangle has 3 medians.
3. The perpendicular line segment from a vertex of a triangle to its opposite side is called an altitude of the triangle. A triangle has 3 altitudes.
4. An exterior angle of a triangle is formed when a side of a triangle is produced. At each vertex, you have two ways of forming an exterior angle.
5. A property of exterior angles:
The measure of any exterior angle of a triangle is equal to the sum of the measures of its interior opposite angles.
6. The angle sum property of a triangle: The total measure of the three angles of a triangle is 180°.
7. A triangle is said to be equilateral if each one of its sides has the same length. In an equilateral triangle, each angle has measure 60°.
8. A triangle is said to be isosceles if atleast any two of its sides are of same length. The non-equal side of an isosceles triangle is called its base; the base angles of an isosceles triangle have equal measure.
9. Property of the lengths of sides of a triangle:
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
The difference between the lengths of any two sides is smaller than the length of the third side.
This property is useful to know if it is possible to draw a triangle when the lengths of the three sides are known.
10. In a right angled triangle, the side opposite to the right angle is called the hypotenuse and the other two sides are called its legs.
11. Pythagoras Property: In a right-angled triangle, the square on the hypotenuse = the sum of the squares on its legs. If a triangle is not right angled this property does not hold good. This property is
useful to decide whether a given triangle is right angled or not.
