![Tilted Squares](/sites/default/files/styles/medium/public/thumbnails/content-id-2293-icon.png?itok=q-hpU9S_)
problem
Tilted Squares
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
![Square It](/sites/default/files/styles/medium/public/thumbnails/content-id-2526-icon.png?itok=ay-_3wou)
problem
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](/sites/default/files/styles/medium/public/thumbnails/content-id-2844-icon.jpg?itok=w-mGVuWn)
problem
Triangles in circles
Can you find triangles on a 9-point circle? Can you work out their angles?
![Semi-regular Tessellations](/sites/default/files/styles/medium/public/thumbnails/content-id-4832-icon.jpg?itok=6M0MIKJs)
problem
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](/sites/default/files/styles/medium/public/thumbnails/content-id-6624-icon.jpg?itok=tQcnV8ND)
problem
Cyclic Quadrilaterals
Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?
![Hidden Squares](/sites/default/files/styles/medium/public/thumbnails/content-id-8485-icon.png?itok=cL1jvQ_x)
![Guess \my Quad](/sites/default/files/styles/medium/public/thumbnails/content-id-11202-icon.png?itok=EPYga5W9)
![Polygon Rings](/sites/default/files/styles/medium/public/thumbnails/content-id-11231-icon.jpg?itok=OSA8CYS6)
![Completing Quadrilaterals](/sites/default/files/styles/medium/public/thumbnails/content-id-11234-icon.png?itok=9HkaYems)
![Polygon Pictures](/sites/default/files/styles/medium/public/thumbnails/content-id-11498-icon.png?itok=6B43GCOU)
problem
Polygon Pictures
Can you work out how these polygon pictures were drawn, and use that to figure out their angles?
![An Equilateral Triangular Problem](/sites/default/files/styles/medium/public/thumbnails/content-id-11501-icon.png?itok=emnLxJyF)
problem
An Equilateral Triangular Problem
Take an equilateral triangle and cut it into smaller pieces. What can you do with them?
![Angles inside](/sites/default/files/styles/medium/public/thumbnails/content-id-13644-icon.jpg?itok=K1ZqqQ9E)
![Parallelogram It](/sites/default/files/styles/medium/public/thumbnails/content-id-15164-icon.png?itok=k-5tuPhA)
problem
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.
![Rhombus It](/sites/default/files/styles/medium/public/thumbnails/content-id-15165-icon.png?itok=1iXhLMGD)
problem
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](/sites/default/files/styles/medium/public/thumbnails/content-id-2667-icon.png?itok=CmvlCxvE)
problem
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](/sites/default/files/styles/medium/public/thumbnails/content-id-2845-icon.png?itok=6LYICzaF)
problem
Subtended angles
What is the relationship between the angle at the centre and the
angles at the circumference, for angles which stand on the same
arc? Can you prove it?
![Right angles](/sites/default/files/styles/medium/public/thumbnails/content-id-2847-icon.png?itok=D0UbxRcI)
problem
Right angles
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
![Shapely pairs](/sites/default/files/styles/medium/public/thumbnails/content-id-2925-icon.png?itok=TRGXNBMk)
problem
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](/sites/default/files/styles/medium/public/thumbnails/content-id-2927-icon.png?itok=oTWSefvP)
problem
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](/sites/default/files/styles/medium/public/thumbnails/content-id-7381-icon.jpg?itok=L6FhgAEP)
problem
Opposite vertices
Can you recreate squares and rhombuses if you are only given a side or a diagonal?
![Quadrilaterals in a Square](/sites/default/files/styles/medium/public/thumbnails/content-id-11105-icon.png?itok=FGW2ReUE)
problem
Quadrilaterals in a Square
What's special about the area of quadrilaterals drawn in a square?
![Star Polygons](/sites/default/files/styles/medium/public/thumbnails/content-id-11456-icon.png?itok=Fu2j0fzE)
problem
Star Polygons
Draw some stars and measure the angles at their points. Can you find and prove a result about their sum?
![Which solids can we make?](/sites/default/files/styles/medium/public/thumbnails/content-id-7306-icon.png?itok=hrHWvpG5)
problem
Which solids can we make?
Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?
![Of all the areas](/sites/default/files/styles/medium/public/thumbnails/content-00-02-six4-icon.png?itok=x3m44zQ0)
problem
Of all the areas
Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?
Image
![Angles, Polygons Stage 3 STEM footer Angles, Polygons Stage 3 STEM footer](/sites/default/files/styles/large/public/thumbnails/content-id-13469-STEMlogo.png?itok=yVOKa-8a)
You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.