Symmetry

Are these statements always true, sometimes true or never true?

This activity investigates how you might make squares and pentominoes from Polydron.

Create a symmetrical fabric design based on a flower motif - and realise it in Logo.

Sketch the graphs for this implicitly defined family of functions.

This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.

Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?

Sketch the graph of $xy(x^2 - y^2) = x^2 + y^2$ consisting of four curves and a single point at the origin. Convert to polar form. Describe the symmetries of the graph.

Given that ABCD is a square, M is the mid point of AD and CP is perpendicular to MB with P on MB, prove DP = DC.

What is the same and what is different about these tiling patterns and how do they contribute to the floor as a whole?