Relationship between the sides of a triangle

Sum of the length of the two sides of a triangle:

The sum of the length of the two sides of a triangle will always be greater than the third side, whether it is an equilateral, isosceles or scalene triangle.

 Sum of the length of the two sides of a triangle

Example :

Check whether it is possible to make a triangle using these measurements or not ?

$$1. 3\:\: cm\:, 4\:\: cm\:, 7\:\: cm$$

We have to check whether the sum of two sides is greater than the third side or not.

$$4 + 7 = 11$$
$$3 + 7 = 10$$
$$3 + 4 =7$$

Here the sum of the two sides is equal to the third side so the triangle is not possible with these measurements.

$$2. 2 \:\:cm\:, 5 \:\:cm\:, 6\:\: cm$$
$$2 + 5 = 7$$
$$6 + 5 =11$$
$$6 + 2 = 8$$

Here the sum of the two sides is greater than the third side so the triangle could be made with these measurements.

Difference between the lengths of two sides of a triangle:

The difference between the lengths of any two sides of a triangle is less than the length of the third side.

For Example:

$$In\:\: ΔABC\:$$,
$$AB – BC < CA \:; BC – AB < CA$$
$$BC – CA < AB \:; CA – BC < AB$$
$$CA – AB < BC \:; AB – CA < BC$$

Altitudes of a triangle:

Altitude is the line segment made by joining the vertex and the perpendicular to the opposite side. Altitude is the height if we take the opposite side as the base.

  Altitudes of a Triangle

The altitude form angle of 90°.There are three altitudes possible in a triangle. The point of intersection of all three altitudes is called the Orthocenter.

Example:

Medians of a triangle:

Median is the line segment which made by joining any vertex of the triangle with the midpoint of its opposite side. The median divides the side into two equal parts.

       Medians of a Triangle  

Every triangle has three medians like AE, CD, and BF in the above triangle. The point where all the three medians intersect each other is called Centroid.