### Great Squares

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

### Just Opposite

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?

### Fitting In

The largest square which fits into a circle is ABCD and EFGH is a square with G and H on the line CD and E and F on the circumference of the circle. Show that AB = 5EF. Similarly the largest equilateral triangle which fits into a circle is LMN and PQR is an equilateral triangle with P and Q on the line LM and R on the circumference of the circle. Show that LM = 3PQ

# Square Bisection

##### Stage: 3 and 4 Short Challenge Level:

Any line which passes though the centre of the square divides the square into two congruent shapes. An example is shown below.

There are an infinite number of suitable lines (lines passing through the centre, at any angle) so there are infinitely many ways the square can be cut in half with a single straight cut.

This problem is taken from the UKMT Mathematical Challenges.
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