1. Compiled by Mr. Lafferty Maths Dept.
Pythagoras Theorem S3
Credit
Investigating Pythagoras Theorem
Finding the length of the smaller side
Solving Real – Life Problems
Pythagoras Theorem Twice
Converse of Pythagoras Theorem
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.

2. Compiled by Mr. Lafferty Maths Dept.
Starter Questions
Q1. Explain why x 5 = 34 and not 50
Q2. Calculate
Q3. Does x2 – 121 factorise to (x – 11) (x - 11)
Q4. The cost of an iPod is £80 including VAT.
How much is the iPod BEFORE VAT.
NON-CALCULATOR
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.

3. Compiled by Mr. Lafferty Maths Dept.
Right – Angle Triangles
Aim of today's Lesson
‘To investigate the right-angle triangle and to come up with a relationship between the lengths of its two shorter sides and the longest side which is called the hypotenuse. ‘
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.

4. Right – Angle Triangles
What is the length of a ? 3
What is the length of b ? 4
Copy the triangle into your jotter
and measure the length of c 5
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.

5. Right – Angle Triangles
What is the length of a ? 6
What is the length of b ? 8
Copy the triangle into your jotter
and measure the length of c 10
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.

6. Right – Angle Triangles
What is the length of a ? 5
What is the length of b ? 12
Copy the triangle into your jotter
and measure the length of c 13
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.

7. Right – Angle Triangles
Copy the table below and fill in the values that are missing a b c a2 b2 c2 3 4 5 12 13 6 8 10
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.

8. Right – Angle Triangles
Can anyone spot a relationship between
a2, b2, c2. a b c a2 b2 c2 3 4 5 9 16 25 12 13
144
169 6 8 10 36 64
100
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.

9. Compiled by Mr. Lafferty Maths Dept.
Pythagoras’s Theorem c b a
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.

10. Compiled by Mr. Lafferty Maths Dept.
Pythagoras’s Theorem x y z
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.

11. Summary of Pythagoras’s Theorem
Note: The equation is ONLY valid for right-angled triangles.
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.

12. Calculating Hypotenuse
Credit
Learning Intention
Success Criteria
Use Pythagoras Theorem to calculate the length of the hypotenuse
“the longest side”
Know the term hypotenuse “ the longest side”
Use Pythagoras Theorem to calculate the hypotenuse.
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.

13. Calculating Hypotenuse
Credit
Two key points when dealing with
right-angled triangles
The longest side in a right-angled triangle is called
The HYPOTENUSE
The HYPOTENUSE is ALWAYS opposite the right angle
c2 = a2 + b2
(xz)2 = (xy)2 + (yz)2 a b c y x z
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.

14. Calculating the Hypotenuse
Example 1
Q2. Calculate the longest length of the right- angled triangle below. c 8 12
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.

15. Calculating the Hypotenuse
Example 2
Q1. An aeroplane is preparing to land at Glasgow Airport. It is over Lennoxtown at present which is 15km from the airport. It is at a height of 8km.
How far away is the plane from the airport? A
LA = 8 G L
Airport
GL = 15
Lennoxtown
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.

16. Calculating Hypotenuse
Credit
Now try
Ex 2.1 and 2.2
MIA Page 147
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.

17. Compiled by Mr. Lafferty Maths Dept.
S3 Starter Questions S3
Credit
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.

18. Length of the smaller side
Credit
Learning Intention
Success Criteria
1. To show how Pythagoras Theorem can be used to find the length of the smaller side.
Use Pythagoras Theorem to find the length of smaller side.
2. Show all working.
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.

19. Length of the smaller side
Credit
To find the length of the smaller side
of a right-angled triangle
we simply rearrange Pythagoras Theorem.
Example : Find the length of side a ?
Check answer ! Always smaller than hypotenuse
20cm
12cm
a cm
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.

20. Length of the smaller side
Credit
Example : Find the length of side a ?
10cm
b cm
8 cm
Check answer ! Always smaller than hypotenuse
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.

21. M N O P C D E F G H I J K L
P(x,y) o r A C Q R S T U V W Z A B

22. Compiled by Mr. Lafferty Maths Dept.
Length of smaller side S3
Credit
Now work through
Ex3.1 and Ex 3.2
Odd Numbers Only
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.

23. Compiled by Mr. Lafferty Maths Dept.
S3 Starter Questions S3
Credit
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.

24. Solving Real – Life Problems Using Pythagoras Theorem
Credit
Learning Intention
Success Criteria
1. To show how Pythagoras Theorem can be used to solve real-life problems.
Apply Pythagoras Theorem to solve real-life problems.
2. Show all working.
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.

25. Solving Real-Life Problems
Credit
When coming across a problem involving finding a missing side in a right-angled triangle, you should consider using Pythagoras’ Theorem to calculate its length.
Example : A steel rod is used to support a tree
which is in danger of falling down.
What is the height of the tree ?
17m 8m
rod a c b
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.

26. Solving Real-Life Problems
Credit
Example 2
A garden has a fence around its perimeter and
along its diagonal as shown below.
What is the length of the fence from D to C. A B
13m 5m D C
b m
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.

27. Compiled by Mr. Lafferty Maths Dept.
Length of smaller side S3
Credit
Now work through
Ex4.1 and Ex 4.2
Odd Numbers Only
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.

28. Compiled by Mr. Lafferty Maths Dept.
S3 Starter Questions S3
Credit
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.

29. Pythagoras Theorem Twice
Credit
Learning Intention
Success Criteria
1. To use knowledge already gained on Pythagoras Theorem to solve harder problems using Theorem twice.
Use the appropriate form of Pythagoras Theorem to solving harder problems.
2. Show all working.
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.

30. Solving Real-Life Problems
Credit
Problem : Find the length of h.
Find length BD first h B C 15 12 A D 13
19-Apr-17

31. Solving Real-Life Problems
Credit
Problem : Find the length of length y.
Now find h h B C 15 12 A D 13
19-Apr-17

32. Solving Real-Life Problems
Credit
Problem : Find the diagonal length of the cuboid AG.
Find AH first F G B C
7cm E H
10cm
6cm A D
8cm
19-Apr-17

33. Solving Real-Life Problems
Credit
Problem : Find the diagonal length of the cuboid AG.
Now find AG F G B C
7cm E H
10cm
6cm A D
8cm
19-Apr-17

34. Compiled by Mr. Lafferty Maths Dept.
Pythagoras Theorem S3
Credit
Now try Ex 5.1
Ch8 (page 154)
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.

35. Compiled by Mr. Lafferty Maths Dept.
S3 Starter Questions S3
Credit
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.

36. Converse of Pythagoras Theorem
Credit
Learning Intention
Success Criteria
1. To explain the converse of Pythagoras Theorem to prove a triangle is right-angled.
Apply the converse of Pythagoras Theorem to prove a triangle is
right-angled.
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.

37. Converse of Pythagoras Theorem
Converse1 – talk
Converse2 – opposite, reverse
Converse of Pythagoras Theorem S3
Credit c
Converse Theorem states that if b a
1. Then triangle MUST be right-angled.
2. Right-angle is directly opposite C.
Hypotenuse
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.

38. Converse of Pythagoras Theorem
Credit
Problem : Is this triangle right-angled ? Explain Answer
If it is then Pythagoras Theorem will be true
10cm
6 cm
9 cm
By the Converse Theorem, triangle is NOT right-angled
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.

39. Converse of Pythagoras Theorem
Credit
Problem : A picture frame manufacturer claims that his
are rectangular is his claim true.
If it is then Pythagoras Theorem will be true
50cm
40 cm
30 cm
By the Converse Theorem, frame IS rectangular
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.

40. Converse of Pythagoras Theorem
Credit
Now try Ex 6.1 & 6.2
Ch8 (page 156)
19-Apr-17
Compiled by Mr. Lafferty Maths Dept.