1. Pythagoras Theorem Reminder of square numbers: 1 2 = 1 x 1 = 1 2 2 = 2 x 2 = 4 3 2 = 3 x 3 = 9 4 2 = 4 x 4 = 16 3232 Base number Index number The index number tells us how many times the base number is multiplied by itself. e.g. 3 4 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. Pythagoras Theorem Square root means think what is multiplied by itself to make this number? Answer these questions: 1 2 3 4 7 9 11 10 Use your calculator to answer these questions: 2.408 5.040 13 20 31.623 90 15 19

3. Pythagoras Theorem c2c2 b2b2 a2a2 a 2 + b 2 = c 2 b a c In a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides. Hypotenuse Pythagoras of Samos (6 C BC)

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

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 a 2 + b 2 = c 2

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

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

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

9. 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 H B L 15 miles 6.4 miles

10. Pythagoras Theorem 12 ft 9.5 ft L 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?