Triangles

Can you sketch triangles that fit in the cells in this grid? Which ones are impossible? How do you know?

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

What does the overlap of these two shapes look like? Try picturing it in your head and then use some cut-out shapes to test your prediction.

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?

Can you find all the different triangles on these peg boards, and find their angles?

This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

Draw some isosceles triangles with an area of $9cm^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?