@ Dr.K.Thiyagu, CUTN1. 2 3 4 Pythagoras Dr.K.Thiyagu, CUTN5.

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Presentation transcript:

@ Dr.K.Thiyagu, CUTN1

2

3

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Pythagoras Dr.K.Thiyagu, CUTN5

This is a right Dr.K.Thiyagu, CUTN6

We call it a right triangle because it contains a right Dr.K.Thiyagu, CUTN7

The measure of a right angle is 90 o 90 Dr.K.Thiyagu, CUTN8

The little square 90 o in the angle tells you it is a right Dr.K.Thiyagu, CUTN9

10

PYTHAGORAS THEOREM Dr.K.Thiyagu, CUTN11

Draw a square on each side. A Pythagorean Dr.K.Thiyagu, CUTN12

c b a Measure the length of each side A Pythagorean Dr.K.Thiyagu, CUTN13

Work out the area of each square. A Pythagorean Puzzle a b C² b² a² Dr.K.Thiyagu, CUTN14

A Pythagorean Puzzle c² b² Dr.K.Thiyagu, CUTN15

A Pythagorean Dr.K.Thiyagu, CUTN16

1  A Pythagorean Dr.K.Thiyagu, CUTN17

1 2  A Pythagorean Dr.K.Thiyagu, CUTN18

1 2  A Pythagorean Dr.K.Thiyagu, CUTN19

1 2 3  A Pythagorean Dr.K.Thiyagu, CUTN20

1 2 3  A Pythagorean Dr.K.Thiyagu, CUTN21

 A Pythagorean Dr.K.Thiyagu, CUTN22

A Pythagorean Dr.K.Thiyagu, CUTN23

A Pythagorean Dr.K.Thiyagu, CUTN24

What does this tell you about the areas of the three squares? The red square and the yellow square together cover the green square exactly. The square on the longest side is equal in area to the sum of the squares on the other two sides. A Pythagorean Dr.K.Thiyagu, CUTN25

Put the pieces back where they came from. A Pythagorean Dr.K.Thiyagu, CUTN26

A Pythagorean Puzzle Put the pieces back where they came Dr.K.Thiyagu, CUTN27

A Pythagorean Puzzle Put the pieces back where they came Dr.K.Thiyagu, CUTN28

A Pythagorean Puzzle Put the pieces back where they came Dr.K.Thiyagu, CUTN29

A Pythagorean Puzzle Put the pieces back where they came Dr.K.Thiyagu, CUTN30

A Pythagorean Puzzle Put the pieces back where they came Dr.K.Thiyagu, CUTN31

This is called Pythagoras’ Theorem. A Pythagorean Puzzle c² b² a² Dr.K.Thiyagu, CUTN32

a 2 + b 2 = c 2 Dr.K.Thiyagu, CUTN33

a a a2a2 b b c c b2b2 c2c2 Let’s look at it this Dr.K.Thiyagu, CUTN34

Pythagoras Theorem c2c2 b2b2 a2a2 a 2 + b 2 = c 2 b a c In a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides. Hypotenuse Pythagoras of Samos (6 C Dr.K.Thiyagu, CUTN35

How to Solve First we needed to find the length of the hypotenuse. 3 4 A C B Dr.K.Thiyagu, CUTN36

How to Solve First we needed to find the length of the hypotenuse. 3 4 A 2 A 2 + B 2 B 2 = C2C2C2C = C2C2C2C = C2C2C2C2 25 = C2C2C2C2 Find the square root of each side. C = 5 A C Dr.K.Thiyagu, CUTN37

3 cm 4 cm x 1 5 cm 12 cm x 2 Pythagoras Theorem x  25x  169x Dr.K.Thiyagu, CUTN38

Pythagoras Theorem 5 cm 6 cm x cm 9.8 cm x Dr.K.Thiyagu, CUTN39

Solve 1.IF AB=12 CM; BC=9CM THEN AC=? 2. IF AB=6 CM; BC= 8 CM THEN Dr.K.Thiyagu, CUTN40

Summary Pythagorean Theorem is A 2 + B 2 = C 2 Now you should have a good idea what the Pythagorean Theorem is and how it works. As you can see it is used in everyday life. We will be doing more work with it later Dr.K.Thiyagu, CUTN41

Assignment Collect the e-resources related to Pythagoras Theorem Try to solve some problem related to Pythagoras Theorem Download some the YouTube videos related to Dr.K.Thiyagu, CUTN42