Can you prove that the sum of the distances of any point inside a square from its sides is always equal?

Can you prove it to be true for a rectangle or a regular hexagon?

Does the hexagon need to be regular?

Can you show the same is the case for a regular pentagon?

Does the pentagon need to be regular?

Creating and manipulating expressions and formulae. Angles - points, lines and parallel lines. Pythagoras' theorem. Investigations. Sine, cosine, tangent. Length/distance. Circle properties and circle theorems. 2D shapes and their properties. Spheres, cylinders & cones. Regular polygons and circles.