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. c 2 = a 2 + b 2 Pythagoras’Theorem a b c

Proof of Pythagoras’Theorem Student Activity

One more Proof & demonstration of Pythagoras’Theorem

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In the right angled triangle ABC, can you spot two other triangles that are similar to it ? By comparing the ratios of the corresponding lengths of the 2 similar triangles, we can lead to the proof that : BC 2 = AB 2 + AC 2 (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 of Pythagoras’ Theorem a b c For any right-angled triangle, c 2 = a 2 + b 2

Worksheet Practice

Qn 1 : Find the length of AC. Hypotenuse A CB Solution : AC 2 = (Pythagoras’ Theorem) AC= AC = 20

Qn 2 : Find the length of QR. Hypotenuse R Q P Solution : 25 2 = QR 2 (Pythagoras’ Theorem) QR 2 = QR= QR= 7

a 2 = (Pythagoras’ Theorem) Qn 3 : Find the value of a a Solution :

Qn 4 : Find the value of b. Solution: 10 2 = b 2 (Pythagoras’ Theorem) 6 10 b

Qn 5 : Find the value of c. Solution: 25 2 = c 2 (Pythagoras’ Theorem) 25 7 c

Qn 6 : Find the length of diagonal d d Solution: d 2 = (Pythagoras’ Theorem)

Qn 7 : Find the length of e. e Solution: 85 2 = e (Pythagoras’ Theorem)

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 A B C Solution : In the figure, AB = 16 BC = 12 AC 2 = AB 2 + BC 2 (Pythagoras’ Theorem) AC 2 = AC 2 = 400 AC = 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 the right-angled triangle ABC. AB = 200 BC = 160 AB 2 = AC 2 + BC 2 (Pythagoras’ Theorem) = AC AC 2 = AC = 120 So, the height of the kite above the ground = AC + Peter’s height = = m 160 m 200 m 1.2 m A B C

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: 13 2 = L 2 (Pythagoras’ Theorem) L 2 = L 2 = 144 L = 12 Find the length of the shadow L. 5 m 13 m L Example 3