1. Pythagoras Theorem
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2. Have you got any I.D. please sir?
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3. Pythagoras Responsible for: 583 B.C. – 500 B.C.
Greek Philosopher and Mathematician
Responsible for:
Formulating and proving the Hypotenuse Theorem which bears his name, Pythagoras Theorem:
a 2 + b 2 = c 2
The most famous theorem in the world
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4. Let’s start at the beginning…
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5. A
Hypotenuse B C
The Hypotenuse is the longer side of a right-angled triangle
The Hypotenuse is opposite the right angle
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6. A
Pythagoras Theorem
In any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides c b B C a
The way we labelled this triangle this means: a 2 b 2 c 2 + =
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7. Finding the hypotenuse62
+ 82
= x2 c x
= x2 c
8 m
100
= x2 c c
100
= x
6 m 10
= x c
x = 10
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8. Finding the hypotenuse82
+ 152
= x2 c x
= x2 c
8 m
289
= x2 c c
289
= x
15 m 17
= x c
x = 17
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9. Finding the hypotenuse82
+ 72
= x2 c x
= x2 c
8 m
113
= x2 c c
113
= x
7 m
10.6
≈ x c
x ≈ 10.6
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10. Finding one of the shorter sides82
+ x 2
= 10 2 c
10 m 64
+ x 2
= 100 c
8 m
x 2
= 100
– 64 c
x 2
= 36 c x
x = 36 c
x =
6 m
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11. Finding one of the shorter sides92
+ x 2
= 14 2 c
14 cm 81
+ x 2
= 196 c x
x 2
= 196
– 81 c
x 2
= 115 c
x =
115 c
9 cm
x ≈
10.7 cm
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12. a geometrical explanation
of the
Pythagorean Theorem
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13. p 2 q 2 r 2 r + = p q = +
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14. x 2 y 2 z 2 z + = x y = +
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15. + = Pythagoras also works geometrically with semicircles
Can you explain why it works with semicircles? + =
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