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Archive for the 'Constructions' Category

Introduction to Constructions

Posted by Robert Chaney on 15th May 2011

Constructions:  the drawing of various shapes using only a compass and straightedge or ruler. No measurement of lengths or angles is allowed.

The word construction in geometry has a very specific meaning: the drawing of geometric items such as lines and circles using only a compass and straightedge or ruler. Very importantly, you are not allowed to measure angles with a protractor, or measure lengths with a ruler.

A Pair of Compasses

Also just called the compass, it is a drawing instrument used for drawing circles and arcs. It has two legs, one with a point and the other with a pencil or lead. You can adjust the distance between the point and the pencil and that setting will remain until you change it. (This kind of compass has nothing to do with the kind used find the North direction when you are lost).

A Straight-edge

A straightedge is simply a guide for the pencil when drawing straight lines. In most cases you will use a ruler for this, since it is the most likely to be available, but you must not use the markings on the ruler during constructions. If possible, turn the ruler over so you cannot see them.

Which ones?

There are 22 constructions in total, although not all of them are needed for some exams. By selecting the relevant category from the drop down window on the left-hand side, a selection of constructions that must be learnt will appear listed.

Resources available

For most of them, you will find a video demonstrating the process, an animation, a step-by-step guide, and a worksheet for you to complete.

Each video is about two minutes long, showing each step with audio commentary.

The animation is flash-based diagramatic visualisation of the process of creating the construction.

The step-by-step guide is a printable record of each step demonstrated in the flash animation.

The worksheet is a printable set of activities to repeat the relevant construction.

Alternatively, open the following CONSTRUCTIONS PDF file which lists each construction depending on your level/certificate, and links to all of these resources.

Happy drawing!

Posted in Constructions, JC - 1st Yr, JC Higher, JC Ordinary, Junior Certificate, LC Foundation, LC Higher, LC Ordinary, Leaving Certificate, Mathematics | No Comments »

Construction 1 – Bisector of a given angle, using only compass and straight edge.

Posted by Robert Chaney on 15th May 2011

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Construction 2 – Perpendicular Bisector of a Line Segment

Posted by Robert Chaney on 15th May 2011

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Construction 3 – Line perpendicular to a given line l, passing through a given point not on l

Posted by Robert Chaney on 15th May 2011

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Construction 4 – Line perpendicular to a given line l, passing through a given point on l

Posted by Robert Chaney on 15th May 2011

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Construction 5 – Line parallel to given line, through given point

Posted by Robert Chaney on 15th May 2011

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Construction 6 – Division of a segment into 2, 3 equal segments, without measuring it

Posted by Robert Chaney on 15th May 2011

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Construction 7 – Division of a segment into any number of equal segments, without measuring it

Posted by Robert Chaney on 15th May 2011

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Construction 8 – Line segment of given length on a given ray

Posted by Robert Chaney on 15th May 2011

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Construction 9 – Angle of given number of degrees with a given ray as one arm

Posted by Robert Chaney on 15th May 2011

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Construction 10 – Triangle, given lengths of three sides

Posted by Robert Chaney on 15th May 2011

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Construction 11 – Triangle, given SAS data

Posted by Robert Chaney on 15th May 2011

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Construction 12 – Triangle, given ASA data

Posted by Robert Chaney on 15th May 2011

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Construction 13 – Right-angled triangle, given the length of the hypotenuse and one other side

Posted by Robert Chaney on 15th May 2011

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