Physics and Maths Tutoring from Michael A Smith.

Most students know of Pythagorus' Theorem, but where does it come from?

Warm-up:

Compound shapes
Practice Questions
Textbook Exercise
(Care of corbettmaths.com)

The Problem:

A small square of side c, inscribed in a larger square of side a + b

A square of side $(a + b)$ has a smaller square of side $c$ inscribed.

Find the area of the big square, the small square and the four triangles in terms of $a$ , $b$ , and $c$ . Use these areas to proof pythagoras' theorem.

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Solution:

The area of one of the triangles is

{Area}_{Triangle} = ½ a b

The area of the large square is

{Area}_{Large} = {(a + b)}^{2}

and for the small

{Area}_{Small} = c^{2}

Using the diagram to aid combining these areas

{Area}_{Large} = {Area}_{Small} + 4 \times {Area}_{Triangle}

{(a + b)}^{2} = c^{2} + 4 \times ½ a b

a^{2} + 2 a b + b^{2} = c^{2} + 2 a b

a^{2} + b^{2} = c^{2}

As required

Proving the Pythagorean theorem

Warm-up:

The Problem:

Solution:

Further Reading: