Proving Pythagoras’ Theorem and that ancient Greeks were pretty good at mathematics.

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Presentation transcript:

Proving Pythagoras’ Theorem and that ancient Greeks were pretty good at mathematics

Who was Pythagoras?

a b c We start with a triangle of a particular type.

Where might you see right angled triangles in use?

a b c What is the area of this rectangle?

What is the formula for the area of a square? What is the formula for the area of a rectangle?

a b c c a b Split that rectangle so that we can have two of the original triangles and a new right angled triangle

How many types of quadrilateral can you name?

a b c c f a b e Fill in the gap with another right angled triangle to make another rectangle.

Can you work out the area of each triangle?

a b c c a b e f Mirror one rectangle to make a larger one

How many lines of symmetry does the large rectangle shown have? Draw a shape with 4 lines of symmetry?

a b c c a e e f Can you work out the area of each set of shapes?

Use what you know to express c in terms of a & b. Clue: c 2 = ?

a b c Pythagoras’ Theorem

Homework: Research Pythagoras and find out something else he is credited with discovering. Bonus Credit: Find an innovative use for Pythagoras’ theorem. Best use presented at the next class gets bonus credit and a special prize…