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Transcript


NO
O M
G E
I T
R R
T Y

CONTENTS PAGE

1. Introduction

3. Thales theorem

2. Trigonometry

4. Pythagoras theorem

5. Al Kashi theorem

INTRODUCTION

TRIGONOMETRY

3 formulas :

adjacent
cos(angle)= hypothenuse

opposite
sin(angle)= hypothenuse
opposite
tan(angle)= adjacent

Mnemonic way :

Soh Cah Toa

THALES THEOREM

PHILOSOPHER

SAVANT

MATHEMATICIAN

GREC

625-620 BC


548-545 BC

THALES THEOREM

Thales "butterfly"

A

B

C

E

D

THALES THEOREM

Thales "butterfly"

A

B

C

E

D

Conditions

- if AB//DE
- if the straight line AD and BE are secant in C

THALES THEOREM

Thales "butterfly"

A

B

C

E

D

Conditions

- if AB//DE
- if the straight line AD and BE are secant in C

"Basic" Thales

A

D

E

B

C

PYTHAGORAS THEOREM

Pythagoras of Samos

Ancient grec philosopher

Born around 570 BC on the island of Samos

He died at Metapontium, in modern-day Italy, around 500 BC

- Right-angle triangle

PYTHAGORAS THEOREM

Condition :

Formula :

BC = BA + AC

2 2 2

A L K A S H I T H E O R E M

A

B

C

a

b

c

A L K A S H I T H E O R E M

A

B

C

a

b

c

C o n d i t i o n s :

- have a triangle
- have two lenghts of two sides and the mesure of one angle


A L K A S H I T H E O R E M

A

B

C

a

b

c

C o n d i t i o n s :

- have a triangle
- have two lenghts of two sides and the mesure of one angle


F o r m u l a :

a = b + c - 2bc cos(Â)


2 2 2

A L K A S H I T H E O R E M

A

B

C

a

b

c

F o r m u l a :

a = b + c - 2bc cos(Â)


?

15 cm

10 cm

45°

2 2 2

T H A N K S