## Cartesian Isometric

The graph below is a coordinate system based on $60$ $^\circ$ angles. It was drawn on isometric paper.

The marked points are $(6, 2)$, $(6, 5)$ and $(9, 2)$. When joined they form an equilateral triangle.

The following five sets of points are also triangles.

A. $(1, 13), (6, 8)$ and $(6, 13)$.

B. $(1, 1), (3, 3)$ and $(7, 1)$.

C. $(12, 1), (17, 1)$ and $(8, 9)$.

D. $(1, 10), (5, 2)$ and $(6, 6)$.

E. $(7, 5), (15, 4)$ and $(7, 11)$.

What kinds of triangles are they?

Can you work out any of the angles at the vertices?

Pupils need to be encouraged to look very carefully at the angles of the triangles. Isometric paper is almost essential.

When you're were working out the angles in the triangles did you notice how the sides cut through the grid triangles?

Learners could make their own graph on isometric paper.