To work with the converse of the Pythagorean Theorem, it would be good to remember that in a right triangle, the sum of the squares of the measures of the legs equals the square of the measure of the hypotenuse or the equation:

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The Pythagorean Theorem

The Converse of the Pythagorean Theorem, if the square of the measure of a side of a triangle is equal to the sum of the square of the other two sides, then the triangle is a right triangle. It can be used to determine if three measurements form a right triangle. The construction field uses the idea of Pythagorean triples. One Pythagorean triple is the 3, 4, 5 triangle. These measurements meet the requirements of a Pythagorean triangle. Any multiple of this 3,4,5 triangle will also be a right triangle. It is pretty neat how that works. Anyway, when building items such as a retaining wall, swimming pool, driveway or home addition, it is important that you are building square to the existing structure. Thus you use a multiple of the 3,4,5, triangle to ensure you are square. The bigger the structure, the larger the multiple you will use.

Back to the objective at hand, the converse of the Pythagorean theorem has two related theorems. These are the triangle inequalities theorems. These inequalities allow us to classify a triangle by it angles, when all we have is information on the sides of the triangles.

If the given sides meet the requirements of this triangle inequality, then the triangle is acute.

Triangle Inequality Acute

If the given sides meet the requirements of this triangle inequality, then the triangle is obtuse.

Triangle Inequality Obtuse

The video goes through two examples and the above theorems. The first example is determining if a triangle is a right triangle. The next example models how to classify the given triangle when given the lengths of the two sides. As always thanks for coming. I hope this information helped. If you need further assistance, leave a comment on the blog. I check in a few times a day. I love math. I might not post something everyday, but I check on my video stats and comments as well as my blog. I know that it is new, but I really like to write about math. Some people may think that is pointless, but someone has to do it.