Flashcards · Maths · Vectors, Constructions and Loci
Ruler-and-Compass Constructions
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What is a construction?
A drawing made with a ruler and compasses, with no protractor.
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What is the perpendicular bisector of a line?
A line that cuts it in half at right angles.
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How do you construct a perpendicular bisector?
Draw matching arcs from both ends that cross twice, and join the crossing points.
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What is true of every point on a perpendicular bisector?
It is the same distance from both ends of the line.
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How do you bisect an angle?
Draw an arc on both arms, then matching arcs from those points, and join the vertex to the crossing.
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What is true of every point on an angle bisector?
It is the same distance from both arms.
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How do you construct a \(60^\circ\) angle?
Draw two arcs of the same radius and join the end to the crossing point.
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How do you construct a \(30^\circ\) angle?
Construct a \(60^\circ\) angle and bisect it.
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How do you construct a triangle from three sides?
Draw one side, then arcs of the other two lengths from its ends.
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Why must you leave the arcs on the drawing?
They show the method, and earn the marks.
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How do you construct a perpendicular from a point to a line?
Arc from the point cutting the line twice, then arcs from those points, and a line through the crossing.
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What is the shortest distance from a point to a line?
The perpendicular distance.
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What instrument do you need for constructions?
A pair of compasses and a ruler.
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Should the compass width stay the same for matching arcs?
Yes.
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What accuracy is usually allowed?
About 2 millimetres.
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What is a bisector?
A line that cuts something into two equal parts.