### Cutting Corners

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

### Four Triangles Puzzle

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

### Transformations on a Pegboard

How would you move the bands on the pegboard to alter these shapes?

# Uncanny Triangles

##### Stage: 2 Challenge Level:

Thomas, Jane and Anna were drawing right angled triangles on squared paper. Their triangles had two sides which were an exact number of squares long and could not be longer than $15$ squares. These are Jane's triangles:

They were calculating the areas of the triangles.

"I've got one triangle where the area and the sum of the lengths of the two shorter sides come to exactly the same number!" exclaimed Anna, "Look, it's that one!"

Thomas looked at his work. "How uncanny - but so have I! But look at it. It's quite a different shape from yours."

What were the measurements of the triangles they had drawn?