Maths: Perpendicular bisectors

I am using a Maths text book called "Maths KS3 Classbook" by Alan Smith.



My chapter today is Geometric Constructions: Using a protractor and ruler to construct triangles, using a compass and ruler to construct a triangle, perpendicular bisectors and angle bisectors.

I have done the whole chapter today but am discussing Perpendicular Bisectors in this particular blog entry.

I looked for a good definition of the word Perpendicular. This is what I found:

Perpendicular Meaning and Definition
(n.) A line at right angles to the plane of the horizon; a vertical line or direction.
(a.) At right angles to a given line or surface; as, the line ad is perpendicular to the line bc.
(a.) Exactly upright or vertical; pointing to the zenith; at right angles to the plane of the horizon; extending in a right line from any point toward the center of the earth.
(n.) A line or plane falling at right angles on another line or surface, or making equal angles with it on each side.

Read more at the source: http://thinkexist.com/dictionary/meaning/perpendicular/

- So its a vertical line that is 90 degrees to a horizontal line.

Looking at the word "bisector":

Bisector Meaning and Definition
(n.) One who, or that which, bisects; esp. (Geom.) a straight line which bisects an angle.

Bisect Meaning and Definition
(v. t.) To cut or divide into two parts.
(v. t.) To divide into two equal parts.

Read more at the source: http://thinkexist.com/dictionary/meaning/perpendicular/
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In the exercise I had to draw a horizontal line AB = 6 cm. Then with a compass, opened at approx 4-5cm (more than half of horizontal line), I marked small arcs that intersect - both below and above the line.

I then had to draw a line joining the midpoint of each of the arc. The result was a PERPENDICULAR BISECTOR which divided the line AB into two (half).

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We also discussed how one could use this in real life. 

One could build a + shaped "wind/sun" shelter for livestock in a field. In such a situation you would create a field compass using short rods joined by a piece of twine that was more than half the distance of the required line 10 or 20 meters. Driving one of the rods into the ground and creating arc with the other both above and below would allow you to create an accurate perpendicular bisector. In this way you could for example recycle used tyres by placing them along both 90 degree lines.

If you stack them like bricks and fill them with either soil or compost (aged droppings?) you can make them quite steady. Build up to approx shoulder height or hip height for say sheep. If you experience high winds or have large livestock that could bump the types over then you can look at bolting the types together or use either metal or wooden poles down the middle of each group of tyres anchoring them to the ground. Its a concept that can be adaptable and fine tuned for your application.

Using tyres means you could be recycling a product that has an extremely long lifespan and there is a huge excess of used tyres.

You could of course also use stone or brick etc. depending of where you live and what your local affordable resource is.

Where we live the majority of livestock have very little to no shelter from the elements. Thy do hide behind rock outcrops or a single rock or in the dunes during harsh windy weather. Sometimes the rain comes down sideways so they don't get wet either. In hot countries, this type of shelter would provide much needed shade.