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Presentation Lesson
Review of Pythagorean
Theorem
Important vocabulary words
are highlighted in red.
• Theorem: A statement that has been proven to
be true based on existing truths. Used mostly
in mathematics.
• Example:
• In MN, trees bloom in March and April. Based
on geographic location of MN and the position
of the earth to the sun.
Pythagorean Theorem
Given a right triangle with sides a and b
and hypotenuse c, a2 + b2 = c2.
b
a
c
This theorem is attributed to
Pythagoras, a Greek mathematician and
philospher who lived circa 580’s BCE.
• Right triangle – a triangle in which one
angle is 90o.
• The hypotenuse is the side of a triangle
with the longest length.
hypotenuse
90o
• Now do Worksheet B to derive
Pythagorean Theorem for yourself.
• Another way to view the Pythagorean
Theorem.
• Find the area of the inside small square,
Asmall. The length of a side of the big
square is 2 and its area is, Abig=4.
• Find x.
x
s=2
(Mazur, 2003, p.9)
• A visual of the Pythagorean Theorem.
(Wikipedia, 2012).
• Use the Pythagorean Theorem to solve
for the unknown side.
x
7
5
x
7
(7)2 + (5)2 = x2
49 + 25 = x2
74 = x2
x = √74
5
x
12
(12)2 + (5)2 = x2
144 + 25 = x2
169 = x2
x = 13
5
A Pythagorean triplet has three integers
for the lengths of the sides of a
triangle. Some examples of triples:
(3,4,6)
( 5, 12, 15)
(7,24,25)
(8,15,17)
• Now consider the case where the
triangle is either a isosceles triangle or
an equilateral triangle. An isosceles
triangle is a triangle with two sides of
equal length. An it’s acute angles are
45o.
• An acute angle is angle that is less than
90o.
acute angles
• The sides of an equilateral triangle all
have equal length. Each angle has 60o.
• Discussion of isosceles triangle.
• Discussion of equilateral triangle.
• Discussion finding the lengths of sides
of similar triangles. A similar triangle
has the same angles, but may have
different lengths of sides. A ratio is
the a number that compares the length
of one side to another side of a triangle.
• Sample word problems.
References:
Wikipedia (2012). Retrieved on 2/24/12 from
http://en.wikipedia.org/wiki/Pythagoras.
Mazur, B. (2003). Imaginary Numbers
(particularly the square root of minus fifteen).
New York: Farrar, Straus and Giroux