1. Pythagoras c² a² b² c a b c² = a² + b² has the same area as the two smaller squares added together. The large square + PYTHAGORAS THEOREM is applied to a Right Angle Triangle

2. Six by Three RAT

3. What is the Hypotenuse The Hypotenuse is the longest side in a RAT R ight A ngled T riangle It is the side you add to a right angle to make a RAT hypotenuse The side opposite the Right Angle is the HYPOTENUSE

4. Pythagoras Theorem 'The square on the hypotenuse is equal to the sum of the squares on the other two sides' In the formulae list for exam this is shown as Theorem of Pythagoras a b c a² + b² = c² 3 4 c If you have a and b, the sides making up the right angle, you can use this formula to work out c a= b= 3 5 5 8 2 7

5. Pythagoras … a, b and c a b a and b are the sides which make up the right angle …… the third side …… c ……… is the hypotenuse c a b a b c a b a b c c c c c Start b a

6. Pythagoras Theorem 0 1 2 3 456 7 89 3²+4² C. ÷ x 25 + On ² - Ans = √ 3 4 c a= b= 3 4 a² + b² = c² Use Use if you have sides round right angle a² + b² = c² or c²= a² + b² a²=3x3=9 3 3 Area of a square side 3 a=3 what is a² b²=4x4=16 Area of a square side 4 b=3 what is b² 4 4 c²= a² + b² 3² + 4² =25 c= √ 25 = 5 Opposite of ² is √ c²=

7. Square and Square Root 0 1 2 3 456 7 89 √Ans C. ÷ x 7.7 + On ² - Ans = √ 59.29 √ ² To find the Area of a square of side Calculate 7.7² 7.7 = Type 59.29 7.7 is called the square root. Square root is the opposite of squaring Area of a square = a² √ 59.29 =7.7 New Example Type 7.7 ² = √ = 59.29 To find length of side calculate √59.29 7.7 ² √ a² = 59.29 a = √59.29= 7.7 Opposite of ² is √ Type

8. Pythagoras Theorem 0 1 2 3 456 7 89 C. ÷ x 0 + On ² - Ans = √ 3.5 61.2 c 3.5 61.2 c² = a² + b² Use When you have both sides of the right angle you ADD the squares c²= a² + b² c= Opposite of ² is √ c²= Start Next = = a= b=

9. Smaller Side 0 1 2 3 456 7 89 √Ans C. ÷ x 3.1 + On ² - Ans = √ 20 a= Start Next = a = 25 a² c² = b² + b = ² ² Show Hypotenuse Add Subtract or Given HYPOTENUSE and one short side ….. SUBTRACT squares Identify a or b using right angle. Click Show Hypotenuse This is side c. Click Subtract

10. Which side 0 1 2 3 456 7 89 √Ans C. ÷ x 2.4 + On ² - Ans = √ 8 a= Know two shorter sides ……. ADD “squres” Start Next = a = 8.9 a² c² = b² + b = ² ² Show Hypotenuse Add Subtract or Given HYPOTENUSE and one short side ….. SUBTRACT squares If you know a and b then ADD. Know Hypotenuse SUBTRACT

11. Pythagoras Theorem 0 1 2 3 456 7 89 C. ÷ x 0 + On ² - Ans = √ 3.5 c c² = a² + b² To use you need to know a and b a= Opposite of ² is √ a²= Start Next = = a b 61.3 When you know c.. the longest side then you subtract a² = c² - b² b² = c² - a² or 3.5 c² = a² + b² a² = c² - b² b² = c² - a²