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Pythagorean Theorem

Pythagorean Theorem. Formal Proof. By Irma Crespo. The Formal Proof. A formal proof of a sentence is a sequence of statements wherein each statement follows the form of the previous statement by a valid argument using the rules of reasoning.

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Pythagorean Theorem

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  1. Pythagorean Theorem Formal Proof By Irma Crespo

  2. The Formal Proof • A formal proof of a sentence is a sequence of statements wherein each statement follows the form of the previous statement by a valid argument using the rules of reasoning. http://math.uncc.edu/~droyster/math3181/notes/hyprgeom/node18.html ISZBCrespo

  3. the given point P new line mperpendicular to l the given line l Review The Rules • Perpendicular Postulate If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line.Larson et. al. Geometry. 2001. ISZBCrespo

  4. The geometric mean of the positive numbers 1 and 25 is 5 because . 1 a 5 x = = 5 25 x b 1 5 = 5 25 Review The Rules Given a =1, b = 25, x = 5 • The Geometric Mean of two positive numbers a and b is the positive number x such that . Larson et. al. Geometry. 2001. Also, solving for x results to the square root of a*b, which is a positive number. Larson et. al. Geometry. 2001. 52 = 1*25 √(52) = √ (1*25) = 5 ISZBCrespo

  5. c a c a = = b d d b Review The Rules Cross multiplication. • Cross Product Property If then, ad = bc. Larson et. al. Geometry. 2001. • Addition Property of Equality If a = b, then a + c = b + c Larson et. al. Geometry. 2001 • Distributive Property If ab + ac, then a( b + c) Larson et. al. Geometry. 2001 • Substitution Property of Equality If a = b, then a can be substituted for b. Larson et. al. Geometry. 2001 ISZBCrespo

  6. AB + BC A B C AC Review The Rules • Segment Addition Postulate If B is between A and C, then AB + BC = AC. Larson et. al. Geometry. 2001. If AB + BC = AC, then B is between A and C. Larson et. al. Geometry. 2001. B ISZBCrespo

  7. Do The Formal Proof Read the directions on the Formal Proof worksheet with Review the Rules images . Make sure to use all the rules we just discussed. Submit the worksheet when finished. ISZBCrespo

  8. Time to Play… ISZBCrespo

  9. Exit Slip • Before you say goodbye to Pythagorean Theorem, what did you learn from this unit? • A sentence is enough. ISZBCrespo

  10. Acknowledgement Larson, Boswell, and Stiff. McDougall Littell : Geometry. 2001. ISZBCrespo

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