How to Use Pythagorean Theorem Converse: Is This a Right Triangle?

A Step-by-step Guide to Using Pythagorean Theorem Converse: Is This a Right Triangle?

Here’s how you can use the Pythagorean theorem converse to determine if a triangle is a right triangle:

Step 1: Identify the Sides of the Triangle:

Determine which side of the triangle is the longest. This side is often referred to as the hypotenuse when you’re dealing with right triangles. Let’s label the sides of the triangle as follows: the longest side is ‘\(c\)’, and the other two sides are ‘\(a\)’ and ‘\(b\)’.

Step 2: Square the Lengths of the Sides:

Square the lengths of all three sides. That is, calculate \(a^2, b^2\), and \(c^2\).

Step 3: Check the Pythagorean Equation:

According to the Pythagorean theorem converse, if the triangle is a right triangle, then \(a^2 + b^2\) should be equal to \(c^2\).

If \(a^2 + b^2 = c^2\), then the triangle is a right triangle.

If \(a^2 + b^2 > c^2\), then the triangle is an acute triangle (all angles are less than \(90\) degrees).

If \(a^2 + b^2 < c^2\), then the triangle is an obtuse triangle (one angle is greater than \(90\) degrees).

And that’s it! By following these steps, you can determine whether a given triangle is a right triangle using the converse of the Pythagorean theorem. Remember that the Pythagorean theorem and its converse only apply to triangles, not other polygons or shapes.