1 of 10 The Pythagorean Theorem © Boardworks 2012.
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1 of 10 The Pythagorean Theorem © Boardworks 2012
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Transcript of 1 of 10 The Pythagorean Theorem © Boardworks 2012.
1 of 10
The Pythagorean Theorem
© Boardworks 2012
2 of 10 © Boardworks 2012
Types of triangles
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Right triangles
A right triangle contains a right angle.
The longest side opposite the right angle is called the hypotenuse.
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Identify the hypotenuse
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The history of the Pythagorean Theorem
The Pythagorean Theorem concerns the relationship between the sides of a right triangle.
Although the Theorem is named after Pythagoras, the result was known to many ancient civilizations, including the Babylonians, Egyptians and Chinese, at least 1000 years before Pythagoras was born.
The theorem is named after the Greek mathematician and philosopher, Pythagoras of Samos.
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The Pythagorean Theorem
The Pythagorean Theorem states that the square formed on the hypotenuse of a right triangle…
…has the same area as the sum of the areas of the squares formed on the other two sides.
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Showing the Pythagorean Theorem
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The Pythagorean Theorem
Label the length of the legs of a right triangle a and b and the hypotenuse c.
The area of the largest square is c × c or c2.
ac
b
a2
The areas of the smaller squares are a2 and b2.c2
b2
The Pythagorean Theorem can be written as:
c2 = a2 + b2
9 of 10 © Boardworks 2012
A proof of the Pythagorean Theorem
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The Pythagorean Theorem
The Pythagorean Theorem states that, for a right triangle with a hypotenuse of length c and legs of lengths a and b:
c2 = a2 + b2a
b
c
The Pythagorean Theorem is used to:
check whether a triangle is right given the lengths of all the sides
find the length of a missing side in a right triangle given the lengths of the other two sides.
