Side 1 2 + Side 2 2 = Hy2...... equation 1
Where, Hy denotes the hypotenuse of the triangle and Side1 and Side2 represent the two perpendicular sides. This relation is true only for a right angles triangle. So, for any triangle to be a right angled triangle, must satisfy the above relation. Once the relation is satisfied, we can say that the two shorter sides are perpendicular to each other. Let us consider an example of a triangle ABC given as follows:
Prove it to be a right angled triangle.
Solution: We have been given a triangle ABC, such that the two shorter sides are of measure 12 units and 5 units and the hypotenuse measures 13 units. Using the relation that we specified for a right angle triangle in equation 1 we have:
Side 1 =12, Side 2 = 5 and Hy = 13
Putting the values of the given quantities in the equation we get:
122 + 52 = 132,
144 + 25 = 169,
169 = 169,
LHS = RHS,
Thus we see that the given triangle satisfies the given relation and so the two shorter sides have an angle of 90 degrees between them. This proves triangle ABC a right - angled triangle.