Proving the Pythagorean theorem

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

Solution:

The area of one of the triangles is

$${\mathrm{Area}}_{\text{Triangle}}=\mathrm{½}ab$$

The area of the large square is

$${\mathrm{Area}}_{\text{Large}}={(a+b)}^2$$

and for the small

$${\mathrm{Area}}_{\text{Small}}=c^2$$

Using the diagram to aid combining these areas

$${\mathrm{Area}}_{\text{Large}}={\mathrm{Area}}_{\text{Small}}+4\times {\mathrm{Area}}_{\text{Triangle}}$$ $${(a+b)}^2=c^2+4\times \mathrm{½}ab$$ $$a^2+2ab+b^2=c^2+2ab$$ $$a^2+b^2=c^2$$

As required

Further Reading:

Pythagorus' Theorem
(Care of thirdspacelearning.com)

GCSE Maths Proof - Revision and Worksheets
(care of mmerevise.co.uk)