Geometry
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.
- is the angle spanned by the lines and .
Example 1
Given the line , construct a angle at and a angle at such that a triangle is formed with a peak . Construct a parallel to the line through .
- 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:
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Draw a long enough line, and mark .
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Construct a ° angle at by first constructing a ° angle, then bisecting it.
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Construct a ° angle at by first constructing a ° angle, then bisecting it.
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Mark the point where the lines along the two angles intersect.
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Construct the parallel to through by constructing a normal on through .
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Then, construct a normal on the normal on at . This is the parallel to .
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