Presentation is loading. Please wait.

Presentation is loading. Please wait.

Squaring a Number To square a number means to :

Similar presentations


Presentation on theme: "Squaring a Number To square a number means to :"— Presentation transcript:

1 Squaring a Number To square a number means to :
“Multiply it by itself” Example : means 9 x 9 = 81 means 10 x 10 = 100

2 Squaring a Number Calculate: a) 2² b) 4² c) 8² d) 1² Find:
2 X 2 = 4 4 X 4 = 16 8 X 8 = 16 1 X 1 = 1 Find: a) 3² + 6² b) 4² + 1² c) 8² + 6² d) 9² + 5² 3 X X 6 4 X X 1 8 X X 6 9 X X 5 = 45 = 17 = 100 = 106

3 Square Root of a number You now know how to find : 92 = 9 x 9 = 81
We can ‘undo’ this by asking “which number, times itself, gives 81” From the top line, the answer is 9 This is expressed as : “the SQUARE ROOT of 81 is 9” or in symbols we write :

4 Square Root of a number Find: a) √36 b)√25 c) √1 d) √144 = 12 = 6 = 5
A = 49cm² This square has an area of 49cm². What is the length of one of the sides? √49 = 7 A = 4cm² This square has an area of 4cm². What is the length of one of the sides? √4 = 2

5 Right – Angle Triangles
In a right angled triangle the side directly across from the right angle is called The Hypotenuse

6 Right – Angle Triangles
Measure the length of a ? 3 4 Measure the length of b ? Complete the triangle and measure the length of c (the hypotenuse) 5

7 Right – Angle Triangles
Measure the length of a ? 6 Measure the length of b ? 8 Complete the triangle and measure the length of C (the hypotenuse) 10

8 Right – Angle Triangles
Measure the length of a ? 5 Measure the length of b ? 12 Complete the triangle and measure the length of c the hypotenuse 13

9 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

10 Pythagoras’s Theorem c b a

11 Summary of Pythagoras’s Theorem
Note: The equation is ONLY valid for right-angled triangles.

12 Pythagoras’s Theorem Calculate the lengths of the hypotenuse in each case c cm c cm 12cm 15cm 9cm 8cm 12cm 16cm c cm

13 Calculating the Hypotenuse
Example 1 Q2. Calculate the longest length of the right- angled triangle below. c 8 12

14 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? Aeroplane c b = 8 Airport a = 15 Lennoxtown

15 Calculating the Hypotenuse
Example 1: Calculate the length of the missing side of this triangle. The Hypotenuse (longest side) 6cm a² + b² = c² 8² + 6² = c² = c² c² = 100 c = √100 = 10 8cm

16 Calculating the Hypotenuse
Example 2: Calculate the length of the missing side of this triangle. 5cm The Hypotenuse (longest side) a² + b² = c² 12² + 5² = c² = c² c² = 169 c = √169 = 13 12cm

17 Solving Real-Life Problems
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 length of the rod? 15m 8m rod

18 Solving Real-Life Problems
Example 2 A garden is rectangular in shape. A fence is to be put along the diagonal as shown below. What is the length of the fence. 10m 15m

19 Length of the smaller side
To find the formula for calculating the length of a smaller side we have to re-arrange Pythagoras’ using the balancing method we learned in our Brackets and equation topic.

20 Length of the smaller side
The Hypotenuse or Longest side What side of the triangle is “c” Length of the smaller side Pythagoras’ Theorem is : a² + b² = c² What if we want to find out a value for a? What we do to one side we have to do to the other a² + b² = c² -b² -b² a² = c² - b² Always ‘take away’ the shorter side from the longest side

21 Length of the smaller side
The Hypotenuse or Longest side What side of the triangle is “c” Length of the smaller side Pythagoras’ Theorem is : a² + b² = c² What if we want to find out a value for b? What we do to one side we have to do to the other a² + b² = c² -a² -a² b² = c² - a² Always ‘take away’ the shorter side from the longest side

22 Length of the smaller side
Always take small side away from hypotenuse when finding a sorter side!!! Example : Find the length of side a ? Check answer ! Always smaller than hypotenuse 20cm 12cm a cm

23 Length of the smaller side
Always take small side away from hypotenuse when finding a sorter side!!! Example : Find the length of side b ? 10cm b cm 8 cm Check answer ! Always smaller than hypotenuse

24 Length of the smaller side
Pythagoras’ Theorem is : a² + b² = c² What if we want to find out a value for a? a² + b² = c² We need to re-arrange Pythagoras’ Theorem to form a² = c² - b² Always ‘take away’ the shorter side from the longest side

25 Length of the smaller side
Example : Find the length of side a ? a² = c² - b² a² = 13² - 12² a² = a² = 25 a = √25 = 5 13cm 12cm a cm

26 Length of the smaller side
Example : Find the length of side b ? b² = c² - a² b² = 15² - 12² b² = b² = 81 a = √81 = 9 15cm b cm 12 cm

27 Pythagoras Theorem Finding hypotenuse c Finding shorter side b c b a
Finding shorter side a


Download ppt "Squaring a Number To square a number means to :"

Similar presentations


Ads by Google