Inside Triangles

How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative


Here is a four by four dotty grid:

Image
Inside Triangles


I have joined three dots on the grid to make a triangle which has one dot inside it:

Image
Inside Triangles


How many different triangles with one dot in the middle can you draw?

How do you know have found them all?

You may like to experiment with the pegboard interactivity below, or you could print off this page of dotty grids to work on.