section 1.5 the pythagorean...
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Section 1.5 The Pythagorean Theorem
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Pythagoras was born in the late 6th century BC on the island of Samos.He was a Greek philosopher and religious leader who was responsible forimportant developments in mathematics, astronomy and the theory ofmusic. Pythagoras is famous also for the fact that he allegedly paid for hisfirst student. Frustrated that no one would listen to his learning, hedecided to "buy" a student.
It is believed that the Egyptians and other ancient cultures used a 345rule in construction. In Egypt, Pythagoras studied with the engineers,known as "rope stretchers", who built the pyramids. They had a rope with12 evenly spaced knots. If the rope was pegged to the ground in thedimensions 345,a right triangle would result. This enabled them to laythe foundations of their buildings accurately.
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What is a right triangle?
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Activity
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For each set...
Arrange the three squares so that they share vertices to form a triangle.
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Find things similar about all three triangles.
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Write addition statements using the sides of the square.
32 + 42 = 52
62 + 82 = 102
52 + 122 = 132
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Right triangle A triangle that contains a right angle (90o)
A
BC
The two shorter sides that make up the right angle are called the legs.
Legs =
The side opposite the right angle (the longest side) is called the hypotenuse.
Hypotenuse =
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Pythagorean Theorem
In any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Area 1 + Area 2 = Area 3
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Examples: Find the area of the square on the third side.
1)
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2)
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Pythagorean Theorem
a
b
c
a2 + b2 = c2
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Examples:Find the missing side in each triangle.
1)
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2)
Round answers as indicated!
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Page 34
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Worksheet