Pythagorean Theorem
•Informal Proof
By Irma Crespo
What do you see?
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Meet Pythagoras
• Known as Pythagoras of
Samos.
• Often described as the first
Pure Mathematician.
• Studied properties of numbers
which would be familiar to
mathematicians today, such as
even and odd numbers,
triangular numbers, perfect
numbers etc.
• Named for his geometric
Pythagorean Theorem.
http://www.gap-system.org/~history/Biographies/Pythagoras.html
www.sciencecastle.com
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Pythagorean Theorem
• In a right triangle, the square of the
length of the hypotenuse (c) is equal to
the sum of the squares of the lengths of
the legs (a and b).
Larson et. al. Geometry. 2001.
leg
c
a
leg
b
c2 = a2 + b2
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A Casual Inquiry
• Informal Proof is a loose style of proof
that outlines the main ideas of a formal
proof with less detail and more clarity.
http://faculty.matcmadison.edu/alehnen/weblogic/logproof.htm#InformalProof
• It is represented in high level sketches
from which formal proofs can be
reconstructed.
http://en.wikipedia.org/wiki/Proof_theory#Formal_and_informal_proof
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Do the Informal Proof
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The Informal Proof
(R. O’Donnell Highlights)
•
Construct the triangle.
Create two points.
Connect the two points
to make a line segment .
Make the circle.
Draw a perpendicular line that
intersects the point on the
circle.
Put a point either above or below the
point on the perpendicular line.
Connect the points with line
segments.
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The Informal Proof
• Label the triangle.
B
• Measure the angles.
A
B
C
• Measure the segments.
AB
A
CB
AC
C
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The Informal Proof
• With your angle measurements, do you
have a 900 angle? What type of triangle
do you have?
• With your segment measurements in
place, follow the worksheet directions on
the computational part to answer each
question. Which one demonstrates the
Pythagorean Theorem?
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Create the Equation
• Group into pairs.
• Bring out your Pythagoras Square worksheet.
• Create an algebraic representation of the image on the
worksheet following the Pythagorean equation.
• Explain the connection between the equation and the
picture. Write the answers on your own worksheets
because these will be graded individually but also jot
down the name of your partner on the worksheet.
• Prepare to explain your answers before the class.
• After discussion, submit the worksheets for grading.
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Exit Slip
• Write a sentence on how you
think Pythagorean Theorem can be
applied.
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Acknowledgement
Larson, Boswell, and Stiff.
McDougall Littell :
Geometry. 2001.
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