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# How to Prove a Triangle is a Right Triangle?

TopA right - angled triangle is a triangle whose angle between the two shorter sides is equal to 90 degrees. It is a diagram whose Geometry is defined by the 3 sides of which two are always perpendicular to each other. So, how to prove a triangle is a Right Triangle? For a triangle to be a right angled triangle we define a theorem called as Pythagorean Theorem. According to this theorem the side that is opposite to the Right Angle is called as the hypotenuse and the relationship between the three sides of the triangle is given as follows:

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.