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Pythagoras Theorem

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What is it?

• If you know two sides of a right angled triangle you can work out the other side.

This is the right angle

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How it works!How it works!

• 'The square on the hypotenuse is equal to the sum of the squares on the other two sides'

The hypotenuse is the longest side. It is always opposite the right angle. Which side is the hypotenuse in this diagram?

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How to find the hypotenuseHow to find the hypotenuse

• The hypotenuse is a

• a2 = b2 + c2

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Worked ExampleWorked Example

• QR2 = QP2 + PR2

• QR2 = 42 + 72

• QR2 = 16 + 49• QR2 = 65• QR = √65• QR = 8.06 cm (this is the longest side so it should be bigger than

the other two sides)

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Other types of questionsOther types of questions

• If it is then Pythagoras should work• YZ should = 10 • YZ2 = 52 + 92

• YZ2 = 25 + 81• YZ2 = 106• YZ = 10.3 cm Is this triangle right angled?

Is this triangle a right angled triangle?

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Other questionsOther questions

• The farmer measured the red line to be 124metres. Is this field a perfect rectangle?

50m

112m

If it is then Pythagoras should work, because there are two right angled triangles in a square or rectangle.

H2 = 502 + 1122

H2 = 2500 + 12,544

H2 = 15,044

H = 122.7 m, Is this field a perfect rectangle?

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Finding the smaller sidesFinding the smaller sides

• Instead of adding, you take the smaller number away from the bigger one

• YZ2 = 82 – 72

• YZ2 = 64 – 49• YZ2 = 15• YZ = 3.9 cm

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Tricky QuestionsTricky Questions

• Find the sloping side of this rubber;

35 mm

10 mm

50 mm

You have to find the right angled triangle and the two sides you need

H2 = 102 + 152

H2 = 100 + 225

H2 = 325

H = 18.02 mm

10 mm

15 mm

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Pythagorean TriplesPythagorean Triples

• These are three numbers that will fit into Pythagoras theorem e.g.

• 3, 4, 5

• 3² + 4² = 5²

• 9 + 16 = 25

• Are these numbers 6, 8, 9 Pythagorean triples?

• No, 100 does not equal 81