This is part of our Secondary Curriculum collection of favourite rich tasks arranged by topic.

Scroll down to see the complete collection, or explore our subcollections on Perimeter and Area in two dimensions, and Surface Area and Volume in three dimensions.

### Completing Quadrilaterals

We started drawing some quadrilaterals - can you complete them?

### Polygon Pictures

Can you work out how these polygon pictures were drawn, and use that to figure out their angles?

### An Equilateral Triangular Problem

Take an equilateral triangle and cut it into smaller pieces. What can you do with them?

### Angles inside

### Parallelogram It

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a parallelogram.

### Quadrilaterals game

### Tilted Squares

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

### Square It

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

### Triangles in circles

Can you find triangles on a 9-point circle? Can you work out their angles?

### Semi-regular Tessellations

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

### Cyclic Quadrilaterals

Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

### Star Polygons

### Rhombus It

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a rhombus.

### Square coordinates

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

### Subtended angles

### Right angles

### Shapely pairs

A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...

### Property chart

A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?

### Opposite vertices

Can you recreate squares and rhombuses if you are only given a side or a diagonal?

### Quadrilaterals in a Square

### Which solids can we make?

### Of all the areas

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*ou may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.*