1. By Irma Crespo Formal Proof

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. 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 new line m perpendicular to l the given point P the given line l

4. Review The Rules The Geometric Mean of two positive numbers a and b is the positive number x such that. Larson et. al. Geometry. 2001. ISZBCrespo a x = b x Given a =1, b = 25, x = 5 The geometric mean of the positive numbers 1 and 25 is 5 because. = 1 525 5 Also, solving for x results to the square root of a*b, which is a positive number. Larson et. al. Geometry. 2001. 1 5 = 25 5 5 2 = 1*25 √ (5 2 ) = √ (1*25) = 5

5. Review The Rules Cross Product Property If then, ad = bc. Larson et. al. Geometry. 2001. ISZBCrespo a b = c d Cross multiplication. a b = c d 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

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

7. Do The Formal Proof ISZBCrespo 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.

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.