2. Simple diagrams and constructions
Most of this section uses the first four buttons and some of the basic options from their dropdown menus – although aspects of a couple of the other buttons will be introduced.
The Pointer toolbox needs to be selected whenever you wish to move around the drawing area without drawing anything.
Text prompts appear on the drawing area – such as ‘this polygon, this angle, circumference of this circle’ – depending on the tool you have selected. These will help you to identify when you have the cursor in the correct position to carry out the required function.
/ To create points left click on the Points Toolbox button. If a single point is not shown on the button, click again to see the dropdown menu – select point. Move the cursor to the drawing area and click wherever you need a point.If you decide to move an object, move the cursor over the object. A hand and text will appear. Left click and hold to ‘grab’ and move the object.
/ To draw lines, select the Lines Toolbox. Click again to see the dropdown menu. Three types of line are available – lines, segments and rays. Select the required type of line. Click once in the drawing area to identify a point the line needs to pass through. Moving the mouse can then specify the direction of the line and left clicking once it is in the correct direction.As the ray and line are constructed using only one point, they can be moved at 15 increments. ‘Grab’ the line as described above, then hold down the shift key as you move the line.
/ To draw a circle, select the Curves Toolbox. If a circle is not shown on the button, click the button again and select Circle from the dropdown menu. Left click in the drawing area where you want the centre of the circle to be then move the mouse to create the circle. Click again once the circle is the required size.
Circles can also be drawn through any two points. Mark two points on a clean page. From the Curves Toolbox select Circle. Move the cursor over the point that is to be the centre of the circle – the text will tell you when you are in the correct position to click the mouse. Then drag out the circle until the cursor is over the point on the circumference. Once again the text will inform you when to click.
If the Arc option is selected, an arc is created through three points – the points plotted are the initial end point, the point identifying the curvature and the final endpoint.
The Conic selection needs five points to be plotted.
Task to try
/ Using the buttons described above create a simple picture like the one below.Don’t forget that a tool remains active until you select a different one. Make sure that you try out the delete facilities.
If you would like to change the thickness or style of the lines go to the Draw toolbox and select either Thickness or Line Style. Both bring up a selection palette. Click on the one you want and then click on the line that is to be changed.
Drawing polygons
Open a new sheet.
Drawing a triangle, polygon or regular polygon is done using the Lines Toolbox. Using the Lines Toolbox dropdown menu, select Triangle. Click on the drawing area for each of the vertices and the triangle will be drawn. If the vertices need to be moved, they can be ‘clicked and grabbed’ then dragged to their new position.
Irregular polygons are completed by selecting polygon from the menu. Click for each of the vertices – but unlike the triangle, the shape needs to be completed by clicking on the original point as well (alternatively double click to complete the polygon . Vertices can be moved as described above.
Selecting Regular Polygon allows for the construction of a regular convex polygon or a star polygon. Click to create or select a centre point then move the cursor until the required radius for the polygon is achieved. The number of sides is shown in the centre of the circle. Move the cursor clockwise from its current position for a convex polygon and counterclockwise for a star polygon. A star polygon will show what looks like a fraction at the centre – the ‘numerator’ gives the number of sides and the ‘denominator’ the number of times the star has crossed.
/ To add text to a diagram, from the Display toolbox select Text. Click on the drawing area where you would like the text to start – then just start typing! You can make the box bigger by positioning the text cursor over the length you want to change – it will change to a double headed arrow - then just dragging the box.To edit text, have the Display toolbox, Text selected. Click on the text and the box will reappear allowing the text to be edited (see next page). If you need to move the text box, click on the Pointer tool, then on the text in order to grab it and move it where you want it.
/ Now have a go at drawing and labelling a diagram – it could look something like this one here.
Modifying text
/ If you wish to change the font size, style, colour at any time, start by selecting the text to be changed. Then go to Options, Font./ This screen should now appear allowing for all the necessary changes to be made.
Click OK when the selections have been made.
The Construct Toolbox
/ Within the Construct toolbox, there are the facilities to construct perpendicular lines, parallel lines, midpoints, perpendicular bisectors and angle bisectors. The steps needed to do these are all explained below.Midpoints
To plot the mid point of any side, select the Construct toolbox, Midpoint. By then clicking anywhere on a line the mid point will be marked.
If a point is required at any point on a line (not the mid point), the Point toolbox, Point on Object needs to be selected. By clicking anywhere on an object that has already been drawn, a point will be created.
A task to try
On a new sheet, draw a quadrilateral. Construct the mid points of each of the sides and using the Lines toolbox, Segment, join the midpoints to form a quadrilateral.
What is the name of the interior quadrilateral? What happens to it when the vertices of the original quadrilateral are dragged?
The Compass tool
/ An alternative way to construct a circle is to select Compass from the Construct toolbox. Then a line segment or two points need to be selected – these determine the radius of the circle. The centre of the circle to be drawn can then be put anywhere on the page just by clicking – the circle will appear as soon as the centre is marked.Parallel and perpendicular lines
On a new sketch, draw a triangle.
To construct a perpendicular to one of the sides, from the Construct toolbox select Perpendicular Line. Select the side it is to be perpendicular to and left click at/on a point the perpendicular is to pass through. For a perpendicular bisector, from the Construct toolbox select Perpendicular Bisector then select the side of the object for which you require the perpendicular bisector.
Constructing parallel lines is done in a very similar way. From the Construct toolbox select Parallel. Select the side it is to be parallel to and click on a point it has to pass through.
To construct a right-angled triangle, draw a line segment on a clean page, construct a perpendicular through one end of the line then mark the third vertex of the triangle with a point on the perpendicular.
/ The diagram will look something like this. We now need to hide the lines that are already drawn so that we can join up the three points as a triangle./ From the Draw toolbox, select Hide/Show and select the two lines by clicking on them. They will become dashed.
Now from the Lines toolbox select Triangle. (The dashed lines will now disappear). Join up the three points.
If you now try to drag the vertices of the triangle, you will see that it always maintains the right angle.
Bisecting an angle
To bisect an angle, select Angle Bisector from the Construct toolbox. Identify the angle you wish to bisect by selecting the three vertices – the vertex of the angle must be the second point selected. The bisector will now appear.
Tasks to try
Now try some constructions – construct an isosceles triangle, rectangle, rhombus, parallelogram …..
The Check Property Toolbox
/ Before starting this section, on a clean page draw a diagram similar to this one.This diagram has a couple of isosceles triangles, parallel lines, perpendicular lines, points on lines, points not on lines etc
/ As the name suggests, this toolbox allows for the properties of points and lines to be checked. Lines can be checked to see if they are parallel or perpendicular, points to see if they are collinear, any three point for equidistance. The Member tool will also check to see whether a point lies on an object or not.
To check whether three points are collinear, select Collinear from the Check Property toolbox. Select any three points that already exist. A box will appear – this can be dragged anywhere on the drawing page. Click and the result of the check will be displayed.
The check for parallel or perpendicular lines is carried out in a similar way. Select Parallel or Perpendicular from the Check Property toolbox. Select any combination of two lines that you wish to check. At this point, the box will appear. Drag it to where you want it; click and the result will be displayed.
Equidistance is also checked in a similar way – but the order in which the points are selected is important. Firstly, select Equidistance from the Check Property toolbox. Now select the three points but remember that the first point selected is checked relative to the remaining two points. The box and text appear as described previously.
If you need to check whether a point lies on an object, the Member tool needs to be selected from the Check Property toolbox. Select the point then select the object. The box and text appear as before.
Use the diagram you drew at the start of this section to try out the functions of the Check Property toolbox.
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