By Irma Crespo

Pythagorean TheoremPythagorean Theorem•Formal Proof

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

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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.

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new line m perpendicular to l the given point P

the given line l

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.

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ax

=bx

Given a =1, b = 25, x = 5

The geometric mean of the positive numbers 1 and 25 is 5 because .

=15 25

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

552 = 1*25

√(52) = √ (1*25)

= 5

Review The Rules• Cross Product Property

If then, ad = bc. Larson et. al. Geometry. 2001.

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ab

=cd

Cross multiplication.

ab

=cd

• 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

Review The Rules• Segment Addition Postulate

If B is between A and C, then AB + BC = AC. Larson et. al. Geometry. 2001.

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If AB + BC = AC, then B is between A and C. Larson et. al. Geometry. 2001.

A B C

BC+AB

AC

B

Do The Formal Proof

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• 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.

Time to Play…

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Exit Slip

• Before you say goodbye to Pythagorean Theorem, what did you learn from this unit?

• A sentence is enough.

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Acknowledgement

Larson, Boswell, and Stiff. McDougall Littell : Geometry. 2001.