The Theorem Of Pythagoras.  Pythagoras was a Greek Mathematician.(580-500B.C). 2500 years old is even older than your teacher.  He was eccentric. (mad!!)

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Presentation transcript:

The Theorem Of Pythagoras.

 Pythagoras was a Greek Mathematician.( B.C) years old is even older than your teacher.  He was eccentric. (mad!!) Don’t mention √ 2 to him!!  He discovered an amazing rule about right angled triangles.  By completing the table opposite you are going to make the discovery for yourself. a b c abca2a2 b2b2 c2c

Complete the results of your table below: abca2a2 b2b2 c2c By considering all the numbers in the completed table can you see what Pythagoras discovered ? The Theorem Of Pythagoras: a 2 + b 2 = c 2

Calculating An Unknown Side.  The longest side of a right angled triangle is called the hypotenuse. a b c a2a2 +b2b2 = c2c2 HYPOTENUSE  Pythagoras discovered that the sum of the squares of the two shorter sides is equal to the square of the hypotenuse.

6 8 A Find the side A in this triangle. Solution. A 2 = A 2 = A 2 = 100 A = √ 100 A =10 Hint Follow this routine exactly every time to solve Pythagoras problems easily.

What Goes In The Box? Find the length of side W in this right angled triangle. W 6.4cm 5.8cm W2W2 = W2W2 = W2W2 =74.6 W=  74.6 W=8.6cm

Find the unknown side in each of the triangles below. 9 (1) 8 A (2) 6 7 B (3) 23 9 C (4) D (5) E

Finding A Shorter Side. 14.7m 12.3m W Calculate the length of side W. W = W = W 2 = – W = √ 64.8 W = 8.05 m

What Goes In The Box? 2 Find the length of side H in the right angled triangle below: H 3.4m 2.6m H2H =3.4 2 H2H =11.56 H2H2 = H2H2 =4.8 H=  4.8 H=2.19m

Calculate the size of the shorter side in the following. 12.4cm (1) 8.3cm A (2) 14.4m 19.8m B (3) 11.2mm 6.7mm C (4) 35.7m 22.6m D (5) 14.7cm 8.6cm E 9.2cm 13.59m 9mm 27.6m 11.9cm