Angles in polygons

Is it possible to find the angles in this rather special isosceles triangle?

Ayah conjectures that the diagonals of a square meet at right angles. Do you agree? How could you find out?

Can you match the Venn diagram with the Carroll diagram that shows the same information?

In this game, you turn over two cards and try to draw a triangle which has both properties.

Here is a selection of different shapes. Can you work out which ones are triangles, and why?

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

Join pentagons together edge to edge. Will they form a ring?

What do you notice when you put three triangles together?

How many triangles have all three angles perfect squares (in degrees)?

This problem shows that the external angles of an irregular hexagon add to a circle.