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# 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?

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Age 7 to 11

Challenge Level

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?

How can the school caretaker be sure that the tree would miss the school buildings if it fell?

Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?