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House of Maths School Workshops Primary & Secondary in Dorset & South - CIRCULAR REASONING: TOP TIPS FOR USING A COMPASS

DO’S AND DON’TS WITH A COMPASS

LEVEL: UP TO GCSE

1. “A PAIR OF COMPASSES”: does not mean you should use two of them! Same comment applies to wearing a pairs of trousers or glasses.

Compass pair of compasses

2.  USE A TEENY WEENY PENCIL: Long pencils get stuck against your hand and prevent the compass moving properly, but a tiny stubby pencil can stay in the compass without getting entangled in your pencil case. If you snap a small piece off the end of another pencil and resharpen the end your Mum will probably not notice. I’ve been using the same compass pencil for years, and it still has plenty of length left.

Compass teeny pencil

3. TO PLACE THE COMPASS at the correct point: hold it right next to the spike – not at the top. Jam the spike hard into the page to stop it slipping. TO DRAW THE ARC: the opposite applies: you now hold it at the top – not on one of the arms and certainly not on both arms at once. Avoid pressing too hard as this can make the compass open up as you draw.

Compass hold here to position, here to draw

4. GCSE students can use CONGRUENT TRIANGLES to see how the constructions work. For instance: we can tell that this angle-bisection works because triangles OAB and OCB are congruent by SSS: so angle AOC=angle COB.

Compass angle bisector

Now use congruent triangles to prove that this construction – DROPPING A PERPENDICULAR FROM POINT ‘P’ TO A LINE – works ok. Scroll down for a hint.

Compass drop a perpendicular

Drop a perpendicular from point P to a line

 

 

HINT: show that triangles PAC and PBC are congruent; deduce that angles APD and BPD are the same; now prove that triangles APD and BPD are congruent. It follows that AD=BD and that the angles at D are all $90^\circ$