>Composite Constructions>Construction of Larger Figures

Construction of Larger Figures

Rule

Instructions for Larger Constructions

1.: Draw a simplified figure from the information in the exercise. Make sure all the information from the exercise is represented in the figure.
2.: Go through the steps of the construction in your head before you start. This way, you can figure out if your strategy will work.
3.: Build the steps such that you always have the information, lines and angles you need for the next step.
4.: It’s smart to start with an angle if one is described in the exercise.
5.: If the distance from a point to a line is given, construct a parallel to the point at that distance.
6.: Larger constructions will test you on the same constructions you’ve done before, and nothing else!
7.: If you know the different methods of construction listed here, then you already have all the tools you need to master the assignment.
8.: Be creative, and try different methods if you’re not certain. You’ll get there!
9.: Even if you’re not sure where to start, do something anyway: Draw a line, find an angle, calculate a side. Just doing something gets your brain going, and other ideas will come to you in due course.
10.: $∠ A B C$ is the angle spanned by the lines $B A$ and $B C$ .

Example 1

Given the line $A B = 7 cm$ , construct a $45 °$ angle at $A$ and a $30 °$ angle at $B$ such that a triangle is formed with a peak $C$ . Construct a parallel to the line $A B$ through $C$ .

1.

Make a simplified figure that is a small copy of what you’re constructing. Mark the angles, lengths and other information.

2.

Begin constructing:

Draw a long enough line, and mark $A B = 7 cm$ .
Construct a $45$ ° angle at $A$ by first constructing a $90$ ° angle, then bisecting it.
Construct a $30$ ° angle at $B$ by first constructing a $60$ ° angle, then bisecting it.
Mark the point $C$ where the lines along the two angles intersect.
Construct the parallel to $A B$ through $C$ by constructing a normal on $A B$ through $C$ .
Then, construct a normal on the normal on $A B$ at $C$ . This is the parallel to $A B$ .

Construction of a triangle and a parallel 1

Construction of a triangle and a parallel 2

Construction of a triangle and a parallel 1

Construction of a triangle and a parallel 2

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Examples of Larger Constructions

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