### At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

### No Right Angle Here

Prove that the internal angle bisectors of a triangle will never be perpendicular to each other.

### A Sameness Surely

Triangle ABC has a right angle at C. ACRS and CBPQ are squares. ST and PU are perpendicular to AB produced. Show that ST + PU = AB

##### Stage: 4 Challenge Level:

Make five different quadrilaterals on a nine-point pegboard, without using the centre peg.

Work out the angles in each quadrilateral you make.

Perhaps checking that the four angles do add up to $360^\circ$!

Now, what other relationships you can see?

For printable sets of circle templates for use with this activity, please see Printable Resources page.

Many thanks to Geoff Faux who introduced us to the merits of the 9 pin circular geo-board.

The boards, moulded in crystal clear ABS that can be used on an OHP (185 cm in diameter), together with a teacher's guide, are available from Geoff at Education Initiatives

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