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Basic construction techniques

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The idea behind drawing different types of angles and lines is to split these into sections and then follow simple instructions in order to construct what is needed. As with most things, the best way to get to grips with constructing shapes is to practise, practise, practise!

We will now guide you through the different techniques needed:

Draw a line perpendicular to another

1) When doing this we must already have the original line and then use just a compass to mark two equal arcs from a centre A.

2) Now we must move the compass to both of these points in turn and draw an arc above and below the line. Starting with the left side we get:

3) You should still have the compass set to the same length and then do the same for the right side.

4) Finally, we need to simply draw a line with a ruler from one cross to the other and this will be a line perpendicular to the original that cuts through the point A.

Draw a triangle when the lengths are given

1) Draw a triangle of side lengths 2cm, 3cm, and 4cm. First, we need to draw the base by drawing a straight line of any of the lengths given. Here we use 4cm.

2) Next, we choose one side of this line and set our compass to one of the other two lengths; here we have done the left-hand side and set the compass to 2cm.

3) Now we draw the final length, 3cm, from the other side of the line and draw an arc that crosses the one above.

4) Finally, we must draw the lines in and these will have the correct length if we use the crossed arcs as the final corner of the triangle.

To draw an angle of exactly  we must do the same steps as above but ensure that all the sides of the triangle are equal, therefore all the angles would be .

Bisect an angle

Bisecting an angle simply means to cut it into two equal angles. This is done with the following steps.

1) First, we are given an angle that we must bisect and, setting our compass to any size, we draw an arc from the point where the lines cross.

2) Now using the two arcs that we have made as a starting point, we must mark out a cross in the centre of the angle.

3) Finally, we draw a line from this point that we have made to the point where the lines meet, which splits the angle into two equal parts. As shown above.

Draw a perpendicular line from a given point

Here we are given a line and a point above this line that we must draw a line from which is perpendicular to the original.

1) We begin by drawing two arcs on the line, with the point as the start, keeping the compass the same length. This is shown below.

2) Now we use these arcs as the start and, keeping the compass at the same length as in step 1, draw a cross below the line.

3) Finally, we must draw a vertical line joining the two crosses. This will be perpendicular to the original line. This is seen above.

Drawing a triangle from given angles

At times we may be told to draw a triangle of any side length, but with specific angle sizes. Say we need to draw a triangle with angles xy and z. This is done as follows.

1) We start by drawing the base of the triangle, which can be any length. And we must draw a line, which is at any one of the angles given, coming away from one end of this line. Do not mark this new line in very hard as we are not sure of the length just yet.

2) Next, we draw one of the remaining two angles from the other side of the original line.

3) Now we can draw the lines fully as we know the third point is where these cross. The final angle (the one at the top) will be equal to the third angle that we were given for the shape.

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