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Great Squares

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

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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?

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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 It

Stage: 3 and 4 Challenge Level: Challenge Level:1

Modbury School sent us some ideas for this activity.

Will said:

Make a triangle with a hollow middle, then fill the middle dot in the top line and wait for the computer to make its desicion.

I think you mean like this:

Then go in the opposite position,
You win, every time you decide you want to win.

George said;

Our soloution is to go three across one down in the centre of your three and when your other opponent goes for one of the squares you will always have another square to go to.

I think you mean something that looks like this:

Yes, that's a very good strategy as it means there are three possible squares to make with your next move (can you see where the three are?).

Thank you all who were involved at Modbury, we hope to hear from you again.