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Gem B Unit 1 Day 4 Notes Pythagorean Theorem and the Distance Formula I. Review of Pythagorean Theorem A. The well-known formula: _____________________________ B. What is it used for? ____________________________________________ _____________________________________________________________ C. To use the Pythagorean Theorem correctly, you must always identify which side “c” is. 1. __________________________________________ 2. __________________________________________ 3. The “____________________________” D. Examples: (answers are given after the last example) 1. Find c. 2. Find a. c 3 10 a 14 6 c = ___________ 3. Find x. a = ________ 4. Find y. x 5 y 15 3 9 x = ______ y = ________ Answers: 3 5, 4 6, 6 2, 5 10 II. Where does the distance formula come from? A. Recall that we said that if a segment extends diagonally across a coordinate grid, that counting blocks will not tell us the length of the segment. 1. 2. B(3, 0) B(6, 4) A(1, 2) C A(-2, -5) C How long is AC? ________ How long is BC ? _______ Find mAB. _______ Find mAB. _______ III. The Distance Formula: _______________________________________________ A. It is a form of the Pythagorean Theorem that accepts coordinates, rather than lengths of sides of triangles. B. Example with diagram. B(10, 10) Find the measure of AB by using the distance formula. A(1, 2) C. Is the segment connecting points A(-2, 5) and B(4, 2) longer, shorter or equal to the line connecting point A with point C(2, 9) ? Show your work and explain how you answered the question. HW: Handout