Pythagoras Theorem Reminder of square numbers 12 22

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

Pythagoras Theorem means think what is multiplied by itself to make this number? Use your calculator to answer Answer these questions: 1 2. 408 2 5. 040 3 13 4 20 7 31. 623 Square root 9 11 90 15 10 19

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

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

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 2 2 2 a +b =c

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

Pythagoras Theorem 3 5 cm x 6 cm 4 x 4. 6 cm 9. 8 cm

Pythagoras Theorem Now do these: 5 11 m 8 xm 25 m 9 m 6 11 cm xm 7 m 23. 8 cm xm 7 3. 4 cm 7. 1 cm x cm

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? H 15 miles B 6. 4 miles Total distance travelled = 21. 4 + 16. 4 = 37. 7 miles 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? 12 ft 9. 5 ft L