1. Find: (to 1.d.p) a)3² = b) 7² = c) 3.45² = d) 9² = e) 10² = f) 20² = g) 2.1 ² = Find: a)√9 = b) √7 = c) √36= d) √2= e) √1.456 = f) √2.5 g) √64 =

2. Find: a)9 b) 49 c) 11.9d) 81 e) 100 f) 400 g) 4.4 Find: a)3 b) 2.6 c) 6 d) 1.4 e) 1.2 f) 1.6 g) 8

3. Criteria for Success To know what Pythagoras theorem is and use it to find the length of the hypotenuse To find out what Pythagoras proved using powers of investigation! To know how to use Pythagoras theorem to show whether a triangle is right-angled.

4. Square Right Angle Prove Hypotenuse Investigate Pythagoras Theorem Keywords Square Root

5. I was born at Samos, in Greece, and lived from 580 to 500 B.C. Now you are going to try to find out what I discovered!! I was a Mathematician who became famous for discovering something unique about right – angled triangles.

6. The longest side opposite the right angle is called the hypotenuse. x a y a z b b c c

7. Make accurate copies of the three right-angled triangles below 4cm 3cm 12cm 5cm 8cm 6cm Next measure the length of the longest side of each one. Then complete the table under activity one on your sheet! abc a2a2a2a2 b2b2b2b2 c2c2c2c2 34 512 68 12 3 4 b a c Can you see a pattern in the last 3 columns? If you can then you have rediscovered Pythagoras’ Theorem

8. So what is Pythagoras’ Theorem? He said that: “For any right triangle, the sum of the areas of the two small squares is equal to the area of the larger.” Pythagoras a 2 + b 2 = c 2 a b c Area A a 2 Area B b 2 Area C c 2

9. We can use Pythagoras’ Theorem to find the longest side in a right – angled triangle Area A 3 2 = 9 Area B 4 2 = 16 Area C 9 +16 = 25 3cm 4cm x Find the Length of side Find the Length of side x How do we get the length of side How do we get the length of side x 25 = 5cm x =  25 = 5cm

10. Find the Length of side Find the Length of side x 7cm 9cm x We can use Pythagoras’ Theorem to find the longest side in a right –angled triangle

11. 1. Complete activity two on your worksheet 2. Complete the questions below 3. Begin activity three! See how far you can get!

12. 5cm 3cm 5.8cm 8cm 7.5cm A. B. 4.5cm One of these is a right-angle, how do we show which one? Now complete activity 3 on the sheet.

13. 8cm x cm 10cm How can we find out the shorter side?

14.  I am able to apply my knowledge of maths to different situations.  I can calculate a missing hypotenuse on a right- angled triangle  I am able to use Pythagoras to identify whether a triangle has a right angle. Next to the title, rate (from 1-5) how confident you feel that you have achieved the learning outcomes. 5 being very confident, and one being not confident at all.