Converse of the Pythagorean theorem

Learning Objectives State the Converse of the Pythagorean theorem in their own words. Use the side lengths of a triangle to determine if it is a right triangle. Differentiate between the Pythagorean theorem and its converse. Apply the Pythagorean Inequalities to classify a triangle as acute, obtuse, or right. First verify that three given side lengths can form a valid triangle using the Triangle Inequality Theorem. Solve geometric and real-world problems by applying the converse of the Pythagorean theorem. You're building a bookshelf and need to make sure the shelves are perfectly perpendicular to the sides. How can you use just a tape measure to guarantee a perfect 90° angle? 📐 You already know how the Pythagorean theorem helps you find a missing side in a right tria...

TermDefinitionExample Pythagorean TheoremIn a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (legs).In a right triangle with legs of 3 cm and 4 cm, the hypotenuse is 5 cm because 3² + 4² = 9 + 16 = 25, and 5² = 25. Converse of the Pythagorean TheoremIf the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.A triangle with side lengths 5, 12, and 13 is a right triangle because 5² + 12² = 25 + 144 = 169, which is equal to 13². HypotenuseThe longest side of a right triangle, located opposite the right angle. When applying the converse, 'c' mu...

Converse of the Pythagorean Theorem Given a triangle with sides a, b, and c, where c is the longest side: If a² + b² = c², then the triangle is a right triangle. Use this rule to prove that a triangle contains a 90-degree angle, making it a right triangle. This is a test for 'rightness'. Pythagorean Inequality for Acute Triangles Given a triangle with sides a, b, and c, where c is the longest side: If a² + b² > c², then the triangle is an acute triangle. Use this rule when the sum of the squares of the two shorter sides is greater than the square of the longest side. This indicates all angles are less than 90 degrees. Pythagorean Inequality for Obtuse Triangles Given a triangle with sides a, b, and c, where c is the longest side: If a² + b² < c², then t...