Pythagoras Theorem

1. Index number Base number Pythagoras Theorem Reminder of square numbers: 32 12 = 1 x 1 = 1 22 = 2 x 2 = 4 32 = 3 x 3 = 9 The index number tells us how many times the base number is multiplied by itself. 42 = 4 x 4 = 16 e.g. 34 means 3 x 3 x 3 x 3 = 81 1,4,9,16, …. are the answers to a number being squared so they are called square numbers.

2. Use your calculator to answer these questions: Answer these questions: Pythagoras Theorem means think what is multiplied by itself to make this number? Square root 1 2.408 2 5.040 3 13 4 20 7 31.623 9 90 11 15 10 19

3. c2 Pythagoras of Samos (6 C BC) c b2 b a a2 Pythagoras Theorem In a right-angled triangle, the square on the hypotenuse is equal to the sumof the squares on the other two sides. Hypotenuse a2+b2 =c2

4. Pythagoras Theorem b q a x y p Cut the squares away from the right angle triangle and cut up the segments of square ‘a’ To show how this works: Draw line segment xy, parallel with the hypotenuse of the triangle Draw line segment pq, at right angles to Line segment xy.

5. Now rearrange them to look like this. You can see that they make a square with length of side ‘c’. This demonstrates that the areas of squares a and b add up to be the area of square c a2+b2 =c2

6. 1 x 3 cm 4 cm = = = x x x 9 + 16 25 169 2 x 5 cm 12 cm Pythagoras Theorem

7. 3 x 5 cm 6 cm 4 x 4.6 cm 9.8 cm Pythagoras Theorem

8. Pythagoras Theorem Now do these: 8 x m 5 11m x m 25 m 9 m 7 m 6 23.8 cm 11 cm x m 7 3.4 cm 7.1 cm x cm

9. 15 miles H B 6.4 miles L Pythagoras Theorem A boat sails due East from a Harbour (H), to a marker buoy (B),15 miles away. At B the boat turns due South and sails for 6.4 miles to a Lighthouse (L). It then returns to harbour. What is the total distance travelled by the boat? Total distance travelled = 21.4 + 16.4 = 37.7 miles

10. 12 ft 9.5 ft L Pythagoras Theorem A 12 ft ladder rests against the side of a house. The top of the ladder is 9.5 ft from the floor. How far is the base of the ladder from the house?