Trigger Activity

Topic of discussion:

Pythagoras’ Theorem

Hypotenuse(it is the side opposite

to the right angle)

For any right-angled triangle, c is the length of the hypotenuse, a and b are the length of the other 2 sides.

c2 = a2 + b2 Pythagoras’Theorem

a

b

c

Pythagoras of Samos

(569 BC - 475 BC )Pythagoras was a Greek philosopher who made importantdevelopments in mathematics, astronomy, and the theory ofmusic.

Proof of

Pythagoras’Theorem

Student Activity

GROUP 1 Workstation No.MUHAMMAD HAZIM B JUMMA'T 1GOH PIAH WEE 2NURUL ATIKAH BTE SALLEH 3CHELSEA SNG KAI KAI 4LUO JIAWEN 5

GROUP 2 Workstation No.MUHAMMAD ZAKWAN B NORALZAHAR 1NURFARAH SYAZWANI BTE RAMLAN 2VEERASINGAM VENKATESHWARAN 3YEO HAO 4NG WAN YIN 5

GROUP 3 Workstation No.LEE HONG LING 1TEO ZHI LIANG 2ZHANG MANG 3JENNIE TAN 4CHEW SIN YONG 5

GROUP 4 Workstation No.FADHEELA BEGUM D/O A R 1TAN KAI MING RYAN 2ONG CHONG MING 3CHANG SHEU CHYUAN 4CHOW JEE CIN 5LEE HIU LAM ELISE 5

GROUP 5 Workstation No.NAJWA BTE AHMAD HAHNEMANN 1ANG WEE CHEONG ANDREW 2GOH KIAN HENG AARON 3U-SA PHALAKORNKITTI 4NG HUI MIN SYLVIA 5MOHAMED IMRAN MARICAN B M M M 5

GROUP 6 Workstation No.NURHAMIZAH BTE OMAR 1RUSHAB NARES SANGHRAJKA 2MUHAMMAD ASRI B MOHD ZAFRULLAH 3ZAFIRAH BTE ABDULLAH 4TAN XIU LI 5MUHAMMAD FARID B FARUS 5

GROUP 7 Workstation No.NORHIDAYU BTE AFANDI 1NUR'SHAZA BTE MUSTAFA 2LIM CHIN CHER GIDEON 3YIK QIAN RU JUNE 4TAN YONG SHUN 5YAPP NICODEMUS 5

One more Proof & demonstration of

Pythagoras’Theorem

Watch this !

In the right angled triangle ABC, can you spot two other triangles that are similar to it ?

By comparing the ratios of the corresponding lengthsof the 2 similar triangles, we can lead to the proofthat : BC2 = AB2 + AC2 (Pythagoras’ Theorem)

Proof using Similar Triangles

Application of

Pythagoras’ Theorem

Locked Out & Breaking In

You’re locked out of your house and the only open window is on the second floor, 4 metres above the ground.

You need to borrow a ladder from your neighbour.

There’s a bush along the edge of the house, so you’ll have to place the ladder 3 metres from the house.

What length of ladder do you need to reach the window ?

Summary ofSummary of

Pythagoras’ TheoremPythagoras’ Theorem

a

bc

For any right-angled triangle,

c2 = a2 + b2

Worksheet Practice

Qn 1 : Find the length of AC.

Hypotenuse

A

CB

16

12Solution :

AC2 = 122 + 162 (Pythagoras’ Theorem)

AC =

AC = 20

22 1612

Qn 2 : Find the length of QR.

HypotenuseR

Q

P

25

24

Solution :

252 = 242 + QR2 (Pythagoras’ Theorem)

QR2 = 252 - 242

QR =

QR = 7

22 2425

a2 = 52 + 122 (Pythagoras’ Theorem)

a

5 12

13

2 2

169

Qn 3 : Find the value of a.

5

12a

Solution :

Qn 4 : Find the value of b .

Solution:

102 = 62 + b2 (Pythagoras’ Theorem)

8

64

610 22

b

6

10

b

Qn 5 : Find the value of c .

Solution:

252 = 72 + c2 (Pythagoras’ Theorem)

c

25 7

24

2 2

576

25

7 c

Qn 6 : Find the length of diagonal d .

10

24 d

Solution:

d2 = 102 + 242 (Pythagoras’ Theorem)

d

10 24

26

2 2

676

Qn 7 : Find the length of e .

e

84 85

Solution:

852 = e2 + 842 (Pythagoras’ Theorem)

e

85 84

13

2 2

169

Applications of

Pythagoras’ Theorem to Word Problems

16km

12km

A car travels 16 km from east to west. Then it turns left and

travels a further 12 km. Find the distance between the starting point and the destination point of the car.

N

?

Example 1

16 km

12 km

AB

C

Solution :

In the figure,AB = 16BC = 12

AC2 = AB2 + BC2 (Pythagoras’ Theorem)AC2 = 162 + 122

AC2 = 400AC = 20

The distance between the starting point and the destination point of the car is 20 km

160 m

200 m

1.2 m

?

Peter, who is 1.2 m tall, is flying a kite at a distance of 160 m from a tree. He has released a string of 200 m long and the kite is vertically above the tree. Find the height of the kite above the ground.

Example 2

Solution :

In the figure, consider theright-angled triangle ABC.

AB = 200BC = 160

AB2 = AC2 + BC2 (Pythagoras’ Theorem)2002 = AC2 + 1602

AC2 = 14400AC = 120

So, the height of the kite above the ground = AC + Peter’s height= 120 + 1.2= 121.2 m

160 m

200 m

1.2 m

A

BC

The height of a tree is 5 m. The distance between the top of it and the tip of its shadow is 13 m.

Solution:

132 = 52 + L2 (Pythagoras’ Theorem)L2 = 132 - 52

L2 = 144L = 12

Find the length of the shadow L.

5 m13 m

L

Example 3