1. Pythagorean Theorem Students will be able to apply the Pythagorean Theorem to solve problems T.2.G.4: Apply the Pythagorean Theorem and its converse in solving practical problems

2. FHS Unit E 2 The Pythagorean Theorem The Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. c 2 = a 2 + b 2 a b c

3. FHS Unit E 3 Using the Pythagorean Theorem Find the value of x. Give your answer in simplest radical form. c 2 = a 2 + b 2 x 2 = 2 2 + 6 2 x 2 = 40 40 4 10 2 2 2 5 2 2 · 5

4. FHS Unit E 4 Converse of the Pythagorean Theorem If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the third side, the triangle is a right triangle. If c 2 = a 2 + b 2, then ΔABC is a right triangle. a b c A B C

5. FHS Unit E 5 TheoremHypothesisConclusion Chord Bisector Theorem In a circle, if a radius is perpendicular to a chord, then it bisects the chord.

6. FHS Unit E 6 Find NP. Step 1: Draw. RN = 17 Step 2: Use Pythagorean Theorem to find NS. NS = 15 Example: Chord Bisector Theorem NP = 2 ∙ NS = 2 ∙ 15 = 30