Converse of the Pythagorean theorem: is it a right triangle?

Learning Objectives State the Converse of the Pythagorean Theorem. Identify the longest side of a given triangle as the potential hypotenuse. Calculate the squares of given side lengths. Apply the Converse of the Pythagorean Theorem to determine if a triangle is a right triangle. Justify their conclusion about a triangle being a right triangle using mathematical reasoning. Distinguish between triangles that are right-angled and those that are not based on side lengths. Imagine you're building a bookshelf 📚. How can you be absolutely sure the corners are perfectly square (90 degrees) without a protractor? In this lesson, you'll discover a powerful tool called the Converse of the Pythagorean Theorem. This theorem allows you to test if any triangle, given its three...

TermDefinitionExample Right TriangleA triangle that has one angle measuring exactly 90 degrees.A triangle with angles 30°, 60°, and 90° is a right triangle. HypotenuseThe longest side of a right triangle, always opposite the right angle.In a 3-4-5 right triangle, the side with length 5 is the hypotenuse. LegsThe two shorter sides of a right triangle that form the right angle.In a 3-4-5 right triangle, the sides with lengths 3 and 4 are the legs. Pythagorean TheoremIn a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the legs (a and b).If a triangle has legs of 3 and 4, then $3^2 + 4^2 = 9 + 16 = 25$. The hypotenuse squared is 25, so the hypotenuse is 5. ConverseA statement formed by swapping the 'if' and 't...

Pythagorean Theorem (Review) $a^2 + b^2 = c^2$ This rule applies *if* you already know a triangle is a right triangle. 'a' and 'b' are the lengths of the legs, and 'c' is the length of the hypotenuse. Converse of the Pythagorean Theorem If $a^2 + b^2 = c^2$, then the triangle is a right triangle. This rule is used to *test* if a triangle is a right triangle when you are given all three side lengths. 'c' must be the longest side, and 'a' and 'b' are the other two sides. Not a Right Triangle Condition If $a^2 + b^2 \neq c^2$, then the triangle is NOT a right triangle. If the sum of the squares of the two shorter sides does not equal the square of the longest side, the triangle does not have a 90-degree angle....