Squares

problem
Opposite vertices

Age

11 to 14

Challenge level

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

Age

11 to 16

Challenge level

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.
problem
Just opposite

Age

14 to 16

Challenge level

A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?
problem
Zig zag

Age

14 to 16

Challenge level

Four identical right angled triangles are drawn on the sides of a square. Two face out, two face in. Why do the four vertices marked with dots lie on one line?
problem
Folding squares

Age

14 to 16

Challenge level

The diagonal of a square intersects the line joining one of the unused corners to the midpoint of the opposite side. What do you notice about the line segments produced?
problem
Semi-detached

Age

14 to 16

Challenge level

A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.
problem
Folding fractions

Age

14 to 16

Challenge level

What fractions can you divide the diagonal of a square into by simple folding?
problem
A tilted square

Age

14 to 16

Challenge level

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
problem
Vector journeys

Age

14 to 18

Challenge level

Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?
problem
A swiss sum

Age

16 to 18

Challenge level

Can you use the given image to say something about the sum of an infinite series?