The document discusses using the Pythagorean theorem to determine if a triangle is a right triangle based on the given side lengths. It provides examples of determining if sets of side lengths form right triangles or not. It also contains practice problems asking the reader to identify if triangles with given side lengths are right triangles using the Pythagorean theorem.

1. Day Two

2. EXAMPLE 3 Identifying Right Triangles Use the converse of the Pythagorean Theorem to determine whether a triangle with the given side lengths is a right triangle. a. a = 6, b = 8, c = 10 a 2 + b 2 c 2 = ? 6 2 + 8 2 10 2 = ? 36 + 64 100 = ? ANSWER A right triangle b. a = 10, b = 12, c = 16 a 2 + b 2 c 2 = ? 10 2 + 12 2 16 2 = ? 100 + 144 256 = ? ANSWER Not a right triangle 100 = 100 244 = 256

5. EXAMPLE 2 Standardized Test Practice SOLUTION c 2 - a 2 = b 2 300 2 - 200 2 = b 2 90,000 – 40,000 = b 2 50,000 = b 2 Pythagorean Theorem Substitute 200 for a and 300 for c . Evaluate powers. Subtract. Take positive square root of each side. Approximate square root. 50,000 = b 2 b 223.6

6. EXAMPLE 2 Standardized Test Practice ANSWER You are about 224 feet above the water. The correct answer is B.