Similarity and congruence

Can you make sense of these three proofs of Pythagoras' Theorem?

Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?

Can you work out the side length of a square that just touches the hypotenuse of a right angled triangle?

Can you make sense of the three methods to work out what fraction of the total area is shaded?

Make your own pinhole camera for safe observation of the sun, and find out how it works.

How would you design the tiering of seats in a stadium so that all spectators have a good view?

Explore the relationships between different paper sizes.

Anamorphic art is used to create intriguing illusions - can you work out how it is done?

What fractions can you divide the diagonal of a square into by simple folding?

Why does this fold create an angle of sixty degrees?