This pattern of floor tiles uses three different shaped tiles, regular octagons, regular quadrilaterals and non-regular hexagons.

What are the angles in each of the shapes?

 

Which of the following statements are true?  Give proofs or counter-examples.

1. A regular polygon has equal sides and equal angles.

2. If a shape has all angles equal then it must be a regular polygon.

3. If a shape has all its sides equal then it must be a regular polygon.

4. If a shape has equal sides then its angles must also be equal.

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