Pythagoras Theorem.

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Presentation transcript:

Pythagoras Theorem

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

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?

How to find the hypotenuse The hypotenuse is a a2 = b2 + c2

Worked Example QR2 = QP2 + PR2 QR2 = 42 + 72 QR2 = 16 + 49 QR2 = 65 QR = 8.06 cm (this is the longest side so it should be bigger than the other two sides)

Other types of questions Is this triangle a right angled triangle? 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?

Other questions The farmer measured the red line to be 124metres. Is this field a perfect rectangle? 112m 50m 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?

Finding 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

Tricky Questions Find the sloping side of this rubber; 35 mm 10 mm 10 mm 15 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

Pythagorean 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